Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. C2×Q8×Dic181 | C2 | semidirect |
| 3. #26041593 | C2 | semidirect |
| 4. #26041590 | C2 | semidirect |
| 5. #26041572 | C2 | semidirect |
| 6. #26041477 | C2 | semidirect |
| 7. #26041418 | C2 | semidirect |
| 8. #26041382 | C2 | semidirect |
| 9. #26041380 | C2 | semidirect |
| 10. #26041333 | C2 | semidirect |
| 11. #448×C181 | C2 | semidirect |
| 104. Q8×C181 | #41 | semidirect |
| 140. C181 | #3112 | semidirect |
| 149. #448 | D181 | semidirect |
| 229. Q8 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041824 | 2 |
| C2×Q8×Dic181 | 2 |
| #26041593 | 2 |
| #26041590 | 2 |
| #26041572 | 2 |
| #26041477 | 2 |
| #26041418 | 2 |
| #26041382 | 2 |
| #26041380 | 2 |
| #26041333 | 2 |
| #448×C181 | 2 |
| #3112 | 181 |