Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 107 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×D41 |
| commutator, socle, cosocle | C22×C41 | C24 |
| Fitting | #127×C41 | C2 |
| hypercenter | #127 | D41 |
| hypocenter | C41 | #550 |
| LCS | G ▷ C22×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10620308 | C2 | semidirect |
| 2. #13050160 | C2 | semidirect |
| 3. #13050136 | C2 | semidirect |
| 4. #13050135 | C2 | semidirect |
| 5. C4×Dic82 | C2 | semidirect |
| 6. C4×D164 | C2 | semidirect |
| 7. D4×Dic41 | C2 | semidirect |
| 8. #127×C41 | C2 | semidirect |
| 42. Dic82 | D4 | semidirect |
| 52. C4×C41 | #41 | semidirect |
| 62. C41 | #550 | semidirect |
| 65. #127 | D41 | semidirect |
| 117. C4 | #10620308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10620308 | 2 |
| #13050160 | 2 |
| #13050136 | 2 |
| #13050135 | 2 |
| C4×Dic82 | 2 |
| C4×D164 | 2 |
| D4×Dic41 | 2 |
| #127×C41 | 2 |
| #550 | 41 |