Finite Group DatabasebetaFinite Group DatabasebetaOrder 22976.
248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 248 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×D359 |
| commutator, socle, cosocle | C22×C359 | C24 |
| Fitting | #123×C359 | C2 |
| prime radical | #26039983 | C2 |
| hypercenter | #123 | D359 |
| hypocenter | C359 | #551 |
| LCS | G ▷ C22×C359 ▷ C359 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26040008 | C2 | semidirect |
| 2. #26040002 | C2 | semidirect |
| 3. #26039997 | C2 | semidirect |
| 4. #26039993 | C2 | semidirect |
| 6. C4×C22⋊D359 | C2 | semidirect |
| 7. #26039973 | C2 | semidirect |
| 8. C22⋊C4×D359 | C2 | semidirect |
| 9. #123×C359 | C2 | semidirect |
| 11. C2×Dic718 | C22 | semidirect |
| 15. C4⋊Dic359 | C22 | semidirect |
| 16. Dic359⋊C4 | C22 | semidirect |
| 17. Dic359⋊C4 | C22 | semidirect |
| 20. C22⋊Dic359 | C22 | semidirect |
| 24. C4×Dic359 | C22 | semidirect |
| 25. C4×Dic359 | C22 | semidirect |
| 27. C22×C4×C359 | C22 | semidirect |
| 28. C4⋊C4×C359 | C22 | semidirect |
| 30. C22⋊C4×C359 | C22 | semidirect |
| 68. C359 | #551 | semidirect |
| 73. #123 | D359 | semidirect |
| 85. C22×C4 | C2×D359 | semidirect |
| 89. C4⋊C4 | C2×D359 | semidirect |
| 97. C22⋊C4 | C2×D359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26040008 | 2 |
| #26040002 | 2 |
| #26039997 | 2 |
| #26039993 | 2 |
| #26039983 | 2 |
| C4×C22⋊D359 | 2 |
| #26039973 | 2 |
| C22⋊C4×D359 | 2 |
| #123×C359 | 2 |
| #551 | 359 |