Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
146 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26041695 | C2 | semidirect |
| 3. #26041099 | C2 | semidirect |
| 4. #26041064 | C2 | semidirect |
| 5. #26041063 | C2 | semidirect |
| 6. C16×Dic181 | C2 | semidirect |
| 7. #504×C181 | C2 | semidirect |
| 71. C181 | #2170 | semidirect |
| 74. #504 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041695 | 2 |
| #26041394 | 2 |
| #26041099 | 2 |
| #26041064 | 2 |
| #26041063 | 2 |
| C16×Dic181 | 2 |
| #504×C181 | 2 |
| #2170 | 181 |