Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1008 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 229 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×#67262 | C2 | semidirect |
| 3. C2×#10625063 | C2 | semidirect |
| 4. #13092420 | C2 | direct (N × H) |
| 5. C2×#10625003 | C2 | semidirect |
| 6. C2×#10625014 | C2 | semidirect |
| 7. C2×#10624991 | C2 | semidirect |
| 8. C2×C23×#102 | C2 | semidirect |
| 14. C2×D4×D23 | C4 | semidirect |
| 18. C22×C8×C23 | C22 | semidirect |
| 19. C2×C4⋊C4×C23 | C22 | semidirect |
| 21. C2×C4⋊Dic23 | C22 | semidirect |
| 23. C22×C23⋊C8 | C22 | semidirect |
| 25. C2×#67262 | C22 | semidirect |
| 27. #10625063 | C22 | semidirect |
| 28. C23×#102 | C22 | semidirect |
| 29. #10625014 | C22 | semidirect |
| 30. #10625003 | C22 | semidirect |
| 31. #10624991 | C22 | semidirect |
| 51. D4×D23 | C2×C4 | semidirect |
| 61. C2×C8×C23 | C23 | semidirect |
| 63. C4⋊C4×C23 | C23 | semidirect |
| 66. C4⋊Dic23 | C23 | semidirect |
| 69. C2×C23⋊C8 | C23 | semidirect |
| 141. C2×#102 | D23 | semidirect |
| 143. C2×C23 | #418 | semidirect |
| 161. C22×C8 | C2×D23 | semidirect |
| 165. C2×C4⋊C4 | C2×D23 | semidirect |
| 171. #102 | C2×D23 | semidirect |
| 172. C23 | C2×#418 | semidirect |
| 205. C2×C8 | C22×D23 | semidirect |
| 209. C4⋊C4 | C22×D23 | semidirect |
| 277. C2 | #13092420 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D23 | 2 |
| C22×#67262 | 2 |
| C2×#10625063 | 2 |
| #13092420 | 2 |
| C2×#10625003 | 2 |
| C2×#10625014 | 2 |
| C2×#10624991 | 2 |
| C2×C23×#102 | 2 |
| C2×#418 | 23 |