Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
616 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 234 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. C22×D181⋊C8 | C2 | semidirect |
| 2. #26042307 | C2 | direct (N × H) |
| 3. C2×C4⋊#13089685 | C2 | semidirect |
| 4. C2×#19153873 | C2 | semidirect |
| 5. C2×C4×#13089685 | C2 | semidirect |
| 8. C2×D181⋊C8 | C22 | semidirect |
| 12. C4⋊#13089685 | C22 | semidirect |
| 13. #19153873 | C22 | semidirect |
| 14. C4×#13089685 | C22 | semidirect |
| 25. C2×#13089685 | D4 | semidirect |
| 30. C2×D724 | C8 | semidirect |
| 46. #13089685 | C2×D4 | semidirect |
| 49. C22×D181 | C2×C8 | semidirect |
| 51. D724 | C2×C8 | semidirect |
| 63. C2×C4×C181 | C2×C8 | semidirect |
| 73. C2×D181 | C22×C8 | semidirect |
| 75. C4×C181 | C22×C8 | semidirect |
| 80. C2×C181 | C8×D4 | semidirect |
| 85. C181 | C2×C8×D4 | semidirect |
| 146. C2×C4 | D181⋊C8 | semidirect |
| 165. C4 | C2×D181⋊C8 | semidirect |
| 167. C2 | #26042307 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D181⋊C8 | 2 |
| #26042307 | 2 |
| C2×C4⋊#13089685 | 2 |
| C2×#19153873 | 2 |
| C2×C4×#13089685 | 2 |
| C2×#19153778 | 2 |
| C2×C8×D4 | 181 |