Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×D724 | C2 | semidirect |
| 2. #26041638 | C2 | semidirect |
| 3. #26041629 | C2 | semidirect |
| 4. #26041574 | C2 | semidirect |
| 5. #26041559 | C2 | semidirect |
| 7. #26041481 | C2 | semidirect |
| 8. #26041410 | C2 | semidirect |
| 9. #26041377 | C2 | semidirect |
| 11. #556×C181 | C2 | semidirect |
| 122. C181 | #3367 | semidirect |
| 124. #556 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D724 | 2 |
| #26041638 | 2 |
| #26041629 | 2 |
| #26041574 | 2 |
| #26041559 | 2 |
| #26041491 | 2 |
| #26041481 | 2 |
| #26041410 | 2 |
| #26041377 | 2 |
| C4×#15668434 | 2 |
| #556×C181 | 2 |
| #3367 | 181 |