Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1008 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×#67267 | C2 | semidirect |
| 3. #13092421 | C2 | direct (N × H) |
| 4. C2×#10624991 | C2 | semidirect |
| 5. C2×C23×#117 | C2 | semidirect |
| 11. C22×D92 | C4 | semidirect |
| 15. C23×#117 | C22 | semidirect |
| 16. C2×C4⋊C4×C23 | C22 | semidirect |
| 20. C2×#67267 | C22 | semidirect |
| 21. C22×C23⋊C8 | C22 | semidirect |
| 22. #10624991 | C22 | semidirect |
| 42. C2×D92 | C2×C4 | semidirect |
| 45. C4⋊C4×C23 | C23 | semidirect |
| 50. C2×C23⋊C8 | C23 | semidirect |
| 95. C2×#117 | D23 | semidirect |
| 99. C2×C23 | #418 | semidirect |
| 115. #117 | C2×D23 | semidirect |
| 116. C2×C4⋊C4 | C2×D23 | semidirect |
| 120. C23 | C2×#418 | semidirect |
| 146. C4⋊C4 | C22×D23 | semidirect |
| 192. C2 | #13092421 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D92 | 2 |
| C22×#67267 | 2 |
| #13092421 | 2 |
| C2×#10624991 | 2 |
| C2×C23×#117 | 2 |
| C2×#418 | 23 |