Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
272 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 77 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. C2×C16×D23 | C2 | semidirect |
| 3. #107×D23 | C2 | semidirect |
| 4. #13092219 | C2 | semidirect |
| 5. #13092218 | C2 | semidirect |
| 6. #13092217 | C2 | semidirect |
| 7. C23×#357 | C2 | semidirect |
| 12. D8×D23 | C4 | semidirect |
| 16. C2×C16×C23 | C22 | semidirect |
| 17. C23×#107 | C22 | semidirect |
| 18. #10625000 | C22 | semidirect |
| 19. C2×C23⋊C16 | C22 | semidirect |
| 31. D8×C23 | C2×C4 | semidirect |
| 39. D184 | C2×C4 | semidirect |
| 88. #357 | D23 | direct (N × H) |
| 94. D23 | #357 | direct (N × H) |
| 105. C2×C16 | C2×D23 | semidirect |
| 108. #107 | C2×D23 | semidirect |
| 109. C23 | C2×#357 | semidirect |
| 122. D8 | C4×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D23 | 2 |
| C2×C16×D23 | 2 |
| #107×D23 | 2 |
| #13092219 | 2 |
| #13092218 | 2 |
| #13092217 | 2 |
| C23×#357 | 2 |
| C2×#357 | 23 |