Finite Group DatabasebetaFinite Group DatabasebetaOrder 3392.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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×D53 |
| commutator, socle, cosocle | C22×C53 | C24 |
| Fitting | C2×C22⋊C4×C53 | C2 |
| hypercenter | C2×C22⋊C4 | D53 |
| hypocenter | C53 | #538 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13133210 | C2 | semidirect |
| 2. #13133203 | C2 | semidirect |
| 3. #13133199 | C2 | semidirect |
| 4. #13133196 | C2 | semidirect |
| 5. #13133191 | C2 | semidirect |
| 6. #13133190 | C2 | semidirect |
| 7. #13133186 | C2 | semidirect |
| 8. C4×C22⋊D53 | C2 | semidirect |
| 9. C2×C22⋊C4×C53 | C2 | semidirect |
| 16. C2×D212 | C22 | semidirect |
| 17. C2×C4×D53 | C22 | semidirect |
| 18. C2×Dic106 | C22 | semidirect |
| 24. #11719921 | C22 | semidirect |
| 25. #11719921 | C22 | semidirect |
| 26. C4⋊Dic53 | C22 | semidirect |
| 27. C4⋊Dic53 | C22 | semidirect |
| 28. #11719919 | C22 | semidirect |
| 29. #11719919 | C22 | semidirect |
| 30. C4×Dic53 | C22 | semidirect |
| 75. C53 | #538 | semidirect |
| 84. C2×C22⋊C4 | D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13133210 | 2 |
| #13133203 | 2 |
| #13133199 | 2 |
| #13133196 | 2 |
| #13133191 | 2 |
| #13133190 | 2 |
| #13133186 | 2 |
| C4×C22⋊D53 | 2 |
| C2×C22⋊C4×C53 | 2 |
| #538 | 53 |