Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26042004 | C2 | semidirect |
| 3. #26041687 | C2 | semidirect |
| 5. #26041573 | C2 | semidirect |
| 6. #26041561 | C2 | semidirect |
| 8. #26041409 | C2 | semidirect |
| 11. #500×C181 | C2 | semidirect |
| 48. #15668438 | Q8 | semidirect |
| 77. Dic362 | C2×Q8 | semidirect |
| 96. C8×C181 | C2×Q8 | semidirect |
| 116. C181 | #3386 | semidirect |
| 121. #500 | 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 |
|---|---|
| #26042004 | 2 |
| #26041944 | 2 |
| #26041687 | 2 |
| #26041582 | 2 |
| #26041573 | 2 |
| #26041561 | 2 |
| #26041556 | 2 |
| #26041409 | 2 |
| #26041378 | 2 |
| C4×#15668438 | 2 |
| #500×C181 | 2 |
| #3386 | 181 |