Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
332 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19153824 | C2 | semidirect |
| 3. #26041278 | C2 | semidirect |
| 4. C2×#19153736 | C2 | semidirect |
| 5. C2×#19153732 | C2 | semidirect |
| 6. #26041043 | C2 | semidirect |
| 7. #343×C181 | C2 | semidirect |
| 11. #19153844 | C4 | semidirect |
| 123. C181 | #1907 | semidirect |
| 130. #343 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153844 | 2 |
| C2×#19153824 | 2 |
| #26041278 | 2 |
| C2×#19153736 | 2 |
| C2×#19153732 | 2 |
| #26041043 | 2 |
| #343×C181 | 2 |
| #1907 | 181 |