Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 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. C2×#19153744 | C2 | semidirect |
| 4. #26041246 | C2 | semidirect |
| 5. #26041043 | C2 | semidirect |
| 6. #26041034 | C2 | semidirect |
| 7. C2×#104×C181 | C2 | semidirect |
| 11. C2×#15668439 | C4 | semidirect |
| 12. C2×#15668437 | C4 | semidirect |
| 13. C2×#15668436 | C4 | semidirect |
| 14. C2×#15668434 | C4 | semidirect |
| 130. C181 | #1876 | semidirect |
| 135. C2×#104 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153836 | 2 |
| C2×#19153824 | 2 |
| C2×#19153744 | 2 |
| #26041246 | 2 |
| #26041043 | 2 |
| #26041034 | 2 |
| C2×#104×C181 | 2 |
| #1876 | 181 |