Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 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. C4⋊Q8×D181 | C2 | semidirect |
| 3. #26041572 | C2 | semidirect |
| 4. #26041568 | C2 | semidirect |
| 5. #26041564 | C2 | semidirect |
| 6. #26041560 | C2 | semidirect |
| 7. #26041556 | C2 | semidirect |
| 8. #26041318 | C2 | semidirect |
| 9. #26041301 | C2 | semidirect |
| 11. #475×C181 | C2 | semidirect |
| 44. #15668450 | Q8 | semidirect |
| 88. D724 | C2×Q8 | semidirect |
| 105. Q8×C181 | C2×Q8 | semidirect |
| 137. C181 | #3079 | semidirect |
| 144. #475 | D181 | semidirect |
| 226. Q8 | Q8×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D181 | 2 |
| C4×#15668450 | 2 |
| #26041572 | 2 |
| #26041568 | 2 |
| #26041564 | 2 |
| #26041560 | 2 |
| #26041556 | 2 |
| #26041318 | 2 |
| #26041301 | 2 |
| #26041279 | 2 |
| #475×C181 | 2 |
| #3079 | 181 |