Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 2. #26041317 | C2 | semidirect |
| 3. #26041107 | C2 | semidirect |
| 4. #26041105 | C2 | semidirect |
| 5. #26041081 | C2 | semidirect |
| 6. #26041081 | C2 | semidirect |
| 7. C22⋊C16×C181 | C2 | semidirect |
| 69. C181 | #2234 | semidirect |
| 77. C22⋊C16 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041515 | 2 |
| #26041317 | 2 |
| #26041107 | 2 |
| #26041105 | 2 |
| #26041081 | 2 |
| C22⋊C16×C181 | 2 |
| #2234 | 181 |