Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 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×#67272 | C2 | semidirect |
| 2. C2×C4×D92 | C2 | semidirect |
| 3. #13092609 | C2 | direct (N × H) |
| 4. C2×C4⋊(C23⋊C8) | C2 | semidirect |
| 5. C2×#10625014 | C2 | semidirect |
| 6. C2×C23×#127 | C2 | semidirect |
| 13. C23×#127 | C22 | semidirect |
| 16. C2×#67272 | C22 | semidirect |
| 21. C4×D92 | C22 | semidirect |
| 22. #10625014 | C22 | semidirect |
| 23. C4⋊(C23⋊C8) | C22 | semidirect |
| 40. C2×D92 | D4 | semidirect |
| 67. C2×C4×C23 | D8 | semidirect |
| 78. D92 | C2×D4 | semidirect |
| 96. C4×C23 | C2×D8 | semidirect |
| 101. C2×#127 | D23 | semidirect |
| 107. C2×C23 | #459 | semidirect |
| 121. #127 | C2×D23 | semidirect |
| 129. C23 | C2×#459 | semidirect |
| 179. C2×C4 | #67272 | semidirect |
| 201. C4 | C2×#67272 | semidirect |
| 207. C2 | #13092609 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67272 | 2 |
| C2×C4×D92 | 2 |
| #13092609 | 2 |
| C2×C4⋊(C23⋊C8) | 2 |
| C2×#10625014 | 2 |
| C2×C23×#127 | 2 |
| C2×#459 | 23 |