Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
336 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #10625124 |
| commutator, cosocle | C42×C23 | C23 |
| Frattini | C42 | C22×D23 |
| Fitting | D42×C23 | C2 |
| socle | C22×C23 | #120 |
| hypercenter | D42 | D23 |
| hypocenter | C23 | #1619 |
| LCS | G ▷ C42×C23 ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ D42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13092793 | C2 | semidirect |
| 2. #13092612 | C2 | semidirect |
| 3. #13092161 | C2 | semidirect |
| 4. D4⋊(C23⋊C8) | C2 | semidirect |
| 5. D42×C23 | C2 | semidirect |
| 13. #10625045 | C22 | semidirect |
| 15. C4⋊(C23⋊C8) | C22 | semidirect |
| 16. C4×C23⋊C8 | C22 | semidirect |
| 45. D4×C23 | D8 | semidirect |
| 70. D42 | D23 | semidirect |
| 91. C23 | #1619 | semidirect |
| 123. D4 | #67272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13092793 | 2 |
| #13092612 | 2 |
| #13092161 | 2 |
| D4⋊(C23⋊C8) | 2 |
| D42×C23 | 2 |
| #1619 | 23 |