Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
384 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 4. #26041571 | C2 | semidirect |
| 5. #26041490 | C2 | semidirect |
| 6. #26041489 | C2 | semidirect |
| 8. #26041373 | C2 | semidirect |
| 9. #26041371 | C2 | semidirect |
| 11. #477×C181 | C2 | semidirect |
| 99. C4×D181 | Q16 | semidirect |
| 132. C181 | #3104 | semidirect |
| 138. #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×Q8×D181 | 2 |
| #26041616 | 2 |
| #26041571 | 2 |
| #26041490 | 2 |
| #26041489 | 2 |
| #26041436 | 2 |
| #26041373 | 2 |
| #26041371 | 2 |
| #26041331 | 2 |
| #477×C181 | 2 |
| #3104 | 181 |