Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 760 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. C22×D184 | C2 | semidirect |
| 2. C22×#67272 | C2 | semidirect |
| 3. C2×#10625111 | C2 | semidirect |
| 4. #13092792 | C2 | direct (N × H) |
| 5. C2×C8×Dic23 | C2 | semidirect |
| 6. C22×D8×C23 | C2 | semidirect |
| 11. C2×D8×C23 | C22 | semidirect |
| 14. #10625111 | C22 | semidirect |
| 16. C2×#67272 | C22 | semidirect |
| 20. C2×D184 | C22 | semidirect |
| 21. C8×Dic23 | C22 | semidirect |
| 37. C2×C8×C23 | D4 | semidirect |
| 42. C2×C23⋊C8 | D4 | semidirect |
| 60. C2×Dic23 | D8 | semidirect |
| 65. C8×C23 | C2×D4 | semidirect |
| 66. C23⋊C8 | C2×D4 | semidirect |
| 80. Dic23 | C2×D8 | semidirect |
| 83. C22×D8 | D23 | semidirect |
| 88. C2×C23 | #493 | semidirect |
| 100. C2×D8 | C2×D23 | semidirect |
| 107. C23 | C2×#493 | semidirect |
| 127. C2×C8 | C22⋊D23 | semidirect |
| 152. C8 | C2×C22⋊D23 | semidirect |
| 168. C2 | #13092792 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D184 | 2 |
| C22×#67272 | 2 |
| C2×#10625111 | 2 |
| #13092792 | 2 |
| C2×C8×Dic23 | 2 |
| C22×D8×C23 | 2 |
| C2×#493 | 23 |