Finite Group DatabasebetaFinite Group DatabasebetaOrder 22976.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26040063 | C2 | semidirect |
| 2. #26040047 | C2 | semidirect |
| 3. #26040046 | C2 | semidirect |
| 4. #26040038 | C2 | semidirect |
| 5. #26040037 | C2 | semidirect |
| 6. Q16×D359 | C2 | semidirect |
| 7. #26040021 | C2 | semidirect |
| 8. C2×Q16×C359 | C2 | semidirect |
| 59. C359 | #578 | semidirect |
| 67. C2×Q16 | D359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26040063 | 2 |
| #26040047 | 2 |
| #26040046 | 2 |
| #26040038 | 2 |
| #26040037 | 2 |
| Q16×D359 | 2 |
| #26040021 | 2 |
| C2×Q16×C359 | 2 |
| #578 | 359 |