Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1224 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 249 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. C24×Dic23 | C2 | semidirect |
| 3. C2×(C22⋊D23)⋊C4 | C2 | semidirect |
| 4. #13092294 | C2 | semidirect |
| 5. #13092289 | C2 | semidirect |
| 6. C22⋊C4×Dic23 | C2 | semidirect |
| 7. C23×#379 | C2 | semidirect |
| 13. C22×C4×D23 | C22 | semidirect |
| 16. #10625124 | C4 | semidirect |
| 18. C2×(C2×D23)⋊C4 | C22 | semidirect |
| 19. C2×Dic23⋊C4 | C22 | semidirect |
| 20. C2×C4×Dic23 | C22 | semidirect |
| 22. C23⋊#95 | C22 | semidirect |
| 25. C24×C23 | C2×C4 | semidirect |
| 32. C2×C22⋊D23 | C2×C4 | semidirect |
| 37. C22×Dic23 | D4 | semidirect |
| 44. C22⋊Dic23 | C2×C4 | semidirect |
| 59. C22×D23 | C22×C4 | semidirect |
| 69. C2×Dic23 | C22×C4 | semidirect |
| 79. C22×C23 | C4×D4 | semidirect |
| 90. Dic23 | #120 | semidirect |
| 96. #379 | D23 | semidirect |
| 118. C23 | C4×#120 | semidirect |
| 122. C24 | C4×D23 | semidirect |
| 177. C22 | (C22⋊D23)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic23 | 2 |
| C2×#10625124 | 2 |
| C2×(C22⋊D23)⋊C4 | 2 |
| #13092294 | 2 |
| #13092289 | 2 |
| C22⋊C4×Dic23 | 2 |
| C23×#379 | 2 |
| C4×#120 | 23 |