Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×Q8×D181 | C2 | semidirect |
| 3. #26041591 | C2 | semidirect |
| 4. #26041575 | C2 | semidirect |
| 5. #26041574 | C2 | semidirect |
| 6. #26041476 | C2 | semidirect |
| 7. #26041416 | C2 | semidirect |
| 8. #26041380 | C2 | semidirect |
| 9. #26041376 | C2 | semidirect |
| 10. #26041335 | C2 | semidirect |
| 11. #460×C181 | C2 | semidirect |
| 87. Dic362 | #41 | semidirect |
| 105. Q8×C181 | #41 | semidirect |
| 140. C181 | #3112 | semidirect |
| 148. #460 | D181 | semidirect |
| 231. Q8 | #15668448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041827 | 2 |
| C4×Q8×D181 | 2 |
| #26041591 | 2 |
| #26041575 | 2 |
| #26041574 | 2 |
| #26041476 | 2 |
| #26041416 | 2 |
| #26041380 | 2 |
| #26041376 | 2 |
| #26041335 | 2 |
| #460×C181 | 2 |
| #3112 | 181 |