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. #26042008 | C2 | semidirect |
| 3. #26041686 | C2 | semidirect |
| 4. #26041682 | C2 | semidirect |
| 6. #26041572 | C2 | semidirect |
| 8. #26041406 | C2 | semidirect |
| 11. #475×C181 | C2 | semidirect |
| 48. #15668436 | Q8 | semidirect |
| 86. #13089678 | C2×Q8 | semidirect |
| 89. Q8×C181 | C2×Q8 | semidirect |
| 116. C181 | #3386 | semidirect |
| 124. #475 | D181 | semidirect |
| 196. Q8 | Q8×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042008 | 2 |
| #26041944 | 2 |
| #26041686 | 2 |
| #26041682 | 2 |
| #26041578 | 2 |
| #26041572 | 2 |
| #26041560 | 2 |
| #26041406 | 2 |
| #26041382 | 2 |
| C4×#15668436 | 2 |
| #475×C181 | 2 |
| #3386 | 181 |