Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D92 |
| commutator, cosocle | C2×C4×C23 | C24 |
| Frattini | C2×C4 | C23×D23 |
| Fitting | C23×#443 | C2 |
| socle | C2×C23 | D42 |
| hypercenter | #443 | D23 |
| hypocenter | C23 | #3293 |
| LCS | G ▷ C2×C4×C23 ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #443 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13093234 | C2 | semidirect |
| 2. #13093231 | C2 | semidirect |
| 3. #13092797 | C2 | semidirect |
| 4. #13092693 | C2 | semidirect |
| 5. #13092692 | C2 | semidirect |
| 6. #13092601 | C2 | semidirect |
| 7. #13092535 | C2 | semidirect |
| 8. C23×#443 | C2 | semidirect |
| 103. #443 | D23 | semidirect |
| 130. C23 | #3293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13093234 | 2 |
| #13093231 | 2 |
| #13092797 | 2 |
| #13092693 | 2 |
| #13092692 | 2 |
| #13092601 | 2 |
| #13092535 | 2 |
| C23×#443 | 2 |
| #3293 | 23 |