Finite Group DatabasebetaFinite Group DatabasebetaOrder 33344.
330 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D521 |
| commutator, socle, cosocle | C22×C521 | C24 |
| Fitting | #120×C521 | C2 |
| hypercenter | #120 | D521 |
| hypocenter | C521 | #525 |
| LCS | G ▷ C22×C521 ▷ C521 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#22552363 | C2 | semidirect |
| 2. C23×Dic521 | C2 | semidirect |
| 3. #30659692 | C2 | semidirect |
| 4. #30659689 | C2 | semidirect |
| 5. #30659685 | C2 | semidirect |
| 6. #30659680 | C2 | semidirect |
| 7. #30659677 | C2 | semidirect |
| 8. D4×Dic521 | C2 | semidirect |
| 9. #30659668 | C2 | semidirect |
| 10. #30659664 | C2 | semidirect |
| 11. #120×C521 | C2 | semidirect |
| 13. C2×Dic1042 | C22 | semidirect |
| 16. C2×C22⋊D521 | C22 | semidirect |
| 22. C22×Dic521 | C22 | semidirect |
| 23. C2×C4×D521 | C22 | semidirect |
| 24. C4⋊Dic521 | C22 | semidirect |
| 25. #22552343 | C22 | semidirect |
| 26. #22552343 | C22 | semidirect |
| 29. C22⋊Dic521 | C22 | semidirect |
| 30. #22552341 | C22 | semidirect |
| 31. C4×Dic521 | C22 | semidirect |
| 46. C2×Dic521 | D4 | semidirect |
| 69. C22×C521 | #41 | semidirect |
| 86. C521 | #525 | semidirect |
| 95. #120 | D521 | semidirect |
| 158. C22 | #22552363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22552363 | 2 |
| C23×Dic521 | 2 |
| #30659692 | 2 |
| #30659689 | 2 |
| #30659685 | 2 |
| #30659680 | 2 |
| #30659677 | 2 |
| D4×Dic521 | 2 |
| #30659668 | 2 |
| #30659664 | 2 |
| #120×C521 | 2 |
| #525 | 521 |