Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
296 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#19153752 | C2 | semidirect |
| 3. #26041287 | C2 | semidirect |
| 5. C2×#19153734 | C2 | semidirect |
| 7. #405×C181 | C2 | semidirect |
| 13. C2×#15668438 | C4 | semidirect |
| 106. C181 | #1977 | semidirect |
| 114. #405 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668438 | 2 |
| C2×#19153752 | 2 |
| #26041287 | 2 |
| #26041283 | 2 |
| C2×#19153734 | 2 |
| C2×#19153732 | 2 |
| #405×C181 | 2 |
| #1977 | 181 |