Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
240 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 95 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×D439 |
| commutator, socle, cosocle | C22×C439 | C24 |
| Fitting | C4×D4×C439 | C2 |
| hypercenter | C4×D4 | D439 |
| hypocenter | C439 | #540 |
| LCS | G ▷ C22×C439 ▷ C439 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28380739 | C2 | semidirect |
| 2. #28380734 | C2 | semidirect |
| 3. #28380726 | C2 | semidirect |
| 4. #28380725 | C2 | semidirect |
| 5. #28380718 | C2 | semidirect |
| 6. #28380717 | C2 | semidirect |
| 7. #28380716 | C2 | semidirect |
| 8. #28380714 | C2 | semidirect |
| 9. C4×D1756 | C2 | semidirect |
| 10. #28380700 | C2 | semidirect |
| 11. C4×D4×C439 | C2 | semidirect |
| 79. C439 | #540 | semidirect |
| 90. C4×D4 | D439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28380739 | 2 |
| #28380734 | 2 |
| #28380726 | 2 |
| #28380725 | 2 |
| #28380718 | 2 |
| #28380717 | 2 |
| #28380716 | 2 |
| #28380714 | 2 |
| C4×D1756 | 2 |
| #28380700 | 2 |
| C4×D4×C439 | 2 |
| #540 | 439 |