Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
334 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 68 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. #26042272 | C2 | semidirect |
| 4. (C2×#10624382)⋊Q8 | C2 | semidirect |
| 5. #26042158 | C2 | semidirect |
| 6. #26042151 | C2 | semidirect |
| 24. #19153849 | C4 | semidirect |
| 26. #19153847 | C4 | semidirect |
| 27. #19153846 | C4 | semidirect |
| 32. #137×C181 | C4 | semidirect |
| 56. C2×Dic362 | C2×C4 | semidirect |
| 73. #15668433 | C2×C4 | semidirect |
| 77. C2×Q8×C181 | C2×C4 | semidirect |
| 80. M16×C181 | C2×C4 | semidirect |
| 153. C181 | #1882 | semidirect |
| 169. #137 | #10624382 | semidirect |
| 200. C2×Q8 | C2×#10624382 | semidirect |
| 221. M16 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042348 | 2 |
| D181⋊#104 | 2 |
| #26042272 | 2 |
| (C2×#10624382)⋊Q8 | 2 |
| #26042158 | 2 |
| #26042151 | 2 |
| #137×D181 | 2 |
| #1882 | 181 |