Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
792 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 1. C23×Dic362 | C2 | semidirect |
| 2. C22×#15668437 | C2 | semidirect |
| 3. #26041417 | C2 | direct (N × H) |
| 4. C2×#19153739 | C2 | semidirect |
| 5. C2×C22⋊#13089678 | C2 | semidirect |
| 11. C22×Dic362 | C22 | semidirect |
| 14. C2×#15668437 | C22 | semidirect |
| 16. #19153739 | C22 | semidirect |
| 17. C22⋊#13089678 | C22 | semidirect |
| 31. C2×Dic362 | D4 | semidirect |
| 58. Dic362 | C2×D4 | semidirect |
| 69. C23×C181 | SD16 | semidirect |
| 93. C22×C181 | C2×SD16 | semidirect |
| 103. C2×C181 | #448 | semidirect |
| 107. C181 | C2×#448 | semidirect |
| 169. C23 | #15668437 | semidirect |
| 201. C22 | C2×#15668437 | semidirect |
| 211. C2 | #26041417 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic362 | 2 |
| C22×#15668437 | 2 |
| #26041417 | 2 |
| C2×#19153739 | 2 |
| C2×C22⋊#13089678 | 2 |
| C2×#121×C181 | 2 |
| C2×#448 | 181 |