Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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×Dic362 | C2 | semidirect |
| 3. #26041688 | C2 | semidirect |
| 4. #26041684 | C2 | semidirect |
| 5. #26041587 | C2 | semidirect |
| 6. #26041575 | C2 | semidirect |
| 11. #446×C181 | C2 | semidirect |
| 48. #15668438 | Q8 | semidirect |
| 115. C181 | #3385 | semidirect |
| 125. #446 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic362 | 2 |
| #26041989 | 2 |
| #26041688 | 2 |
| #26041684 | 2 |
| #26041587 | 2 |
| #26041575 | 2 |
| #26041570 | 2 |
| #26041560 | 2 |
| #26041381 | 2 |
| C4×#15668438 | 2 |
| #446×C181 | 2 |
| #3385 | 181 |