Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 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×D724 | C2 | semidirect |
| 2. #26041689 | C2 | semidirect |
| 3. #26041675 | C2 | semidirect |
| 4. #26041576 | C2 | semidirect |
| 5. #26041569 | C2 | semidirect |
| 6. #26041566 | C2 | semidirect |
| 7. #26041559 | C2 | semidirect |
| 8. #26041410 | C2 | semidirect |
| 11. #554×C181 | C2 | semidirect |
| 47. #15668434 | Q8 | semidirect |
| 84. #13089678 | C2×Q8 | semidirect |
| 89. D4×C181 | C2×Q8 | semidirect |
| 121. C181 | #3384 | semidirect |
| 123. #554 | D181 | semidirect |
| 204. D4 | Q8×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D724 | 2 |
| #26041689 | 2 |
| #26041675 | 2 |
| #26041576 | 2 |
| #26041569 | 2 |
| #26041566 | 2 |
| #26041559 | 2 |
| #26041410 | 2 |
| #26041389 | 2 |
| C4×#15668434 | 2 |
| #554×C181 | 2 |
| #3384 | 181 |