Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1212 conjugacy classes of subgroups; only the 509 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 509 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D23 |
| commutator, socle, cosocle | C22×C23 | C25 |
| Frattini | C22 | C24×D23 |
| Fitting | C22×C42×C23 | C2 |
| hypercenter | C22×C42 | D23 |
| hypocenter | C23 | #3444 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C42 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13092974 | C2 | semidirect |
| 2. #13092967 | C2 | semidirect |
| 3. #13092951 | C2 | semidirect |
| 4. #13092928 | C2 | semidirect |
| 5. C4×#67288 | C2 | semidirect |
| 6. C22×C42×C23 | C2 | semidirect |
| 18. #10625047 | C22 | semidirect |
| 19. #10625046 | C22 | semidirect |
| 20. #10625045 | C22 | semidirect |
| 21. C4×D92 | C22 | semidirect |
| 22. #10625043 | C22 | semidirect |
| 23. C42×D23 | C22 | semidirect |
| 24. #10625041 | C22 | semidirect |
| 25. #10625040 | C22 | semidirect |
| 26. C4×Dic46 | C22 | semidirect |
| 55. C2×C4×C23 | #41 | semidirect |
| 79. C22×C42 | D23 | semidirect |
| 103. C23 | #3444 | semidirect |
| 137. C2×C4 | #67288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13092974 | 2 |
| #13092967 | 2 |
| #13092951 | 2 |
| #13092928 | 2 |
| C4×#67288 | 2 |
| C22×C42×C23 | 2 |
| #3444 | 23 |