Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #10625110 |
| commutator, cosocle | C42×C23 | C23 |
| Frattini | C42 | C22×D23 |
| Fitting | C23×#459 | C2 |
| socle | C22×C23 | #121 |
| hypercenter | #459 | D23 |
| hypocenter | C23 | #1687 |
| LCS | G ▷ C42×C23 ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13092793 | C2 | semidirect |
| 2. #13092612 | C2 | semidirect |
| 3. #13092495 | C2 | semidirect |
| 4. #13092167 | C2 | semidirect |
| 5. #13092161 | C2 | semidirect |
| 6. #13092160 | C2 | semidirect |
| 7. C23×#459 | C2 | semidirect |
| 69. C23⋊C8 | D8 | semidirect |
| 89. #459 | D23 | semidirect |
| 115. C23 | #1687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13092793 | 2 |
| #13092612 | 2 |
| #13092495 | 2 |
| #13092167 | 2 |
| #13092161 | 2 |
| #13092160 | 2 |
| C23×#459 | 2 |
| #1687 | 23 |