Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
384 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 5. #26041572 | C2 | semidirect |
| 6. #26041487 | C2 | semidirect |
| 8. Q16×Dic181 | C2 | semidirect |
| 9. #26041371 | C2 | semidirect |
| 88. C2×Dic181 | Q16 | semidirect |
| 127. C181 | #3104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041831 | 2 |
| C2×Q8×Dic181 | 2 |
| #26041615 | 2 |
| #26041612 | 2 |
| #26041572 | 2 |
| #26041487 | 2 |
| #26041435 | 2 |
| Q16×Dic181 | 2 |
| #26041371 | 2 |
| #26041329 | 2 |
| #451×C181 | 2 |
| #3104 | 181 |