Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
170 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 43 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. #26041717 | C2 | semidirect |
| 2. #26041715 | C2 | semidirect |
| 3. #26041654 | C2 | semidirect |
| 4. #26041395 | C2 | semidirect |
| 5. #26041099 | C2 | semidirect |
| 6. #26041091 | C2 | semidirect |
| 7. #361×C181 | C2 | semidirect |
| 26. Dic724 | D4 | semidirect |
| 30. D1448 | D4 | semidirect |
| 77. C181 | #2213 | semidirect |
| 85. #361 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041717 | 2 |
| #26041715 | 2 |
| #26041654 | 2 |
| #26041395 | 2 |
| #26041099 | 2 |
| #26041091 | 2 |
| #361×C181 | 2 |
| #2213 | 181 |