Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 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. #26041321 | C2 | semidirect |
| 5. #26041148 | C2 | semidirect |
| 6. #26041040 | C2 | semidirect |
| 7. #343×C181 | C2 | semidirect |
| 20. #19153742 | C4 | semidirect |
| 48. C4×Dic181 | C2×C4 | semidirect |
| 54. M16×C181 | C2×C4 | semidirect |
| 61. Dic362 | C4⋊C4 | semidirect |
| 63. D724 | C4⋊C4 | semidirect |
| 112. C181 | #1859 | semidirect |
| 119. #343 | D181 | semidirect |
| 155. M16 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041760 | 2 |
| #26041321 | 2 |
| C2×#19153742 | 2 |
| #26041281 | 2 |
| #26041148 | 2 |
| #26041040 | 2 |
| #343×C181 | 2 |
| #1859 | 181 |