Finite Group DatabasebetaFinite Group DatabasebetaOrder 22976.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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×D359 |
| commutator, socle, cosocle | C22×C359 | C24 |
| Fitting | #124×C359 | C2 |
| prime radical | #26039986 | C2 |
| hypercenter | #124 | D359 |
| hypocenter | C359 | #529 |
| LCS | G ▷ C22×C359 ▷ C359 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26040008 | C2 | semidirect |
| 2. #26040007 | C2 | semidirect |
| 3. #26039997 | C2 | semidirect |
| 4. #26039991 | C2 | semidirect |
| 6. Q8×Dic359 | C2 | semidirect |
| 7. D4×Dic359 | C2 | semidirect |
| 8. (C22⋊D359)⋊C4 | C2 | semidirect |
| 9. #26039971 | C2 | semidirect |
| 10. C42×D359 | C2 | semidirect |
| 11. #124×C359 | C2 | semidirect |
| 74. C359 | #529 | semidirect |
| 78. #124 | D359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26040008 | 2 |
| #26040007 | 2 |
| #26039997 | 2 |
| #26039991 | 2 |
| #26039986 | 2 |
| Q8×Dic359 | 2 |
| D4×Dic359 | 2 |
| (C22⋊D359)⋊C4 | 2 |
| #26039971 | 2 |
| C42×D359 | 2 |
| #124×C359 | 2 |
| #529 | 359 |