Finite Group DatabasebetaFinite Group DatabasebetaOrder 22976.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26040014 | C2 | semidirect |
| 2. #26040010 | C2 | semidirect |
| 3. #26040004 | C2 | semidirect |
| 4. #26040001 | C2 | semidirect |
| 5. #26039997 | C2 | semidirect |
| 6. #26039995 | C2 | semidirect |
| 8. Q8×Dic359 | C2 | semidirect |
| 9. #26039977 | C2 | semidirect |
| 10. #26039974 | C2 | semidirect |
| 11. C22⋊Q8×C359 | C2 | semidirect |
| 73. C359 | #542 | semidirect |
| 81. C22⋊Q8 | D359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26040014 | 2 |
| #26040010 | 2 |
| #26040004 | 2 |
| #26040001 | 2 |
| #26039997 | 2 |
| #26039995 | 2 |
| #26039989 | 2 |
| Q8×Dic359 | 2 |
| #26039977 | 2 |
| #26039974 | 2 |
| C22⋊Q8×C359 | 2 |
| #542 | 359 |