Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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. #26041566 | C2 | semidirect |
| 3. #26041358 | C2 | semidirect |
| 4. #26041032 | C2 | semidirect |
| 5. #26041028 | C2 | semidirect |
| 6. #26041023 | C2 | semidirect |
| 7. #486×C181 | C2 | semidirect |
| 82. C181 | #1697 | semidirect |
| 84. #486 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041566 | 2 |
| #26041471 | 2 |
| #26041358 | 2 |
| #26041032 | 2 |
| #26041028 | 2 |
| #26041023 | 2 |
| #486×C181 | 2 |
| #1697 | 181 |