Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
196 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 3. #26041021 | C2 | semidirect |
| 4. #26041020 | C2 | semidirect |
| 5. #330×C181 | C2 | semidirect |
| 56. C181 | #1534 | semidirect |
| 62. #330 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×D181 | 2 |
| #26041334 | 2 |
| #26041021 | 2 |
| #26041020 | 2 |
| #330×C181 | 2 |
| #1534 | 181 |