Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 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. #26042007 | C2 | semidirect |
| 3. #26041688 | C2 | semidirect |
| 4. #26041684 | C2 | semidirect |
| 6. #26041575 | C2 | semidirect |
| 7. #26041565 | C2 | semidirect |
| 11. #446×C181 | C2 | semidirect |
| 49. #15668438 | Q8 | semidirect |
| 78. Dic362 | C2×Q8 | semidirect |
| 96. C8×C181 | C2×Q8 | semidirect |
| 116. C181 | #3386 | semidirect |
| 126. #446 | D181 | semidirect |
| 213. C8 | Q8×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042007 | 2 |
| Q8×D724 | 2 |
| #26041688 | 2 |
| #26041684 | 2 |
| #26041580 | 2 |
| #26041575 | 2 |
| #26041565 | 2 |
| #26041560 | 2 |
| #26041381 | 2 |
| C4×#15668438 | 2 |
| #446×C181 | 2 |
| #3386 | 181 |