Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
402 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. C2×#19153741 | C2 | semidirect |
| 4. #26041184 | C2 | semidirect |
| 5. #26041041 | C2 | semidirect |
| 6. #26041033 | C2 | semidirect |
| 12. C2×#15668437 | C4 | semidirect |
| 31. C2×Dic362 | C2×C4 | semidirect |
| 42. C2×#13089678 | C2×C4 | semidirect |
| 78. C2×Dic181 | SD16 | semidirect |
| 133. C181 | #1877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668437 | 2 |
| C2×D4×Dic181 | 2 |
| C2×#19153741 | 2 |
| #26041184 | 2 |
| #26041041 | 2 |
| #26041033 | 2 |
| C2×#102×C181 | 2 |
| #1877 | 181 |