Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26041834 | C2 | semidirect |
| 3. #26041588 | C2 | semidirect |
| 4. #26041582 | C2 | semidirect |
| 5. #26041566 | C2 | semidirect |
| 6. #26041564 | C2 | semidirect |
| 7. #26041560 | C2 | semidirect |
| 8. #26041316 | C2 | semidirect |
| 9. C4⋊C8×D181 | C2 | semidirect |
| 11. #477×C181 | C2 | semidirect |
| 44. #15668450 | Q8 | semidirect |
| 134. C181 | #3076 | semidirect |
| 140. #477 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| C4×#15668450 | 2 |
| #26041588 | 2 |
| #26041582 | 2 |
| #26041566 | 2 |
| #26041564 | 2 |
| #26041560 | 2 |
| #26041316 | 2 |
| C4⋊C8×D181 | 2 |
| #26041274 | 2 |
| #477×C181 | 2 |
| #3076 | 181 |