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. #26040062 | C2 | semidirect |
| 3. #26040048 | C2 | semidirect |
| 4. #26040047 | C2 | semidirect |
| 5. #26040044 | C2 | semidirect |
| 6. #26040036 | C2 | semidirect |
| 7. #26040035 | C2 | semidirect |
| 8. C2×#19153331 | C2 | semidirect |
| 9. Q16×D359 | C2 | semidirect |
| 10. #26040023 | C2 | semidirect |
| 11. #137×C359 | C2 | semidirect |
| 87. C359 | #578 | semidirect |
| 94. #137 | D359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26040063 | 2 |
| #26040062 | 2 |
| #26040048 | 2 |
| #26040047 | 2 |
| #26040044 | 2 |
| #26040036 | 2 |
| #26040035 | 2 |
| C2×#19153331 | 2 |
| Q16×D359 | 2 |
| #26040023 | 2 |
| #137×C359 | 2 |
| #578 | 359 |