Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
5758 conjugacy classes of subgroups; only the 1208 normal subgroups are shown.
This group has 5758 conjugacy classes of subgroups — too many to draw. Only its 1208 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. C23×#63243 | C2 | semidirect |
| 2. C23×C4×#595 | C2 | semidirect |
| 3. C22×#10587548 | C2 | direct (N × H) |
| 7. C22×#63243 | C22 | semidirect |
| 10. C22×C4×#595 | C22 | semidirect |
| 11. C2×#10587548 | C22 | direct (N × H) |
| 14. C22×#63254 | C4 | semidirect |
| 16. C23×Dic34 | C4 | semidirect |
| 20. C23×D4×C17 | C4 | semidirect |
| 26. C22×D4×C17 | C2×C4 | semidirect |
| 37. C2×#63254 | C2×C4 | semidirect |
| 44. C22×Dic34 | C2×C4 | semidirect |
| 47. C2×C4×#595 | C23 | semidirect |
| 49. C2×#63243 | C23 | semidirect |
| 50. #10587548 | C23 | direct (N × H) |
| 60. C2×D4×C17 | C22×C4 | semidirect |
| 73. #63254 | C22×C4 | semidirect |
| 81. C2×Dic34 | C22×C4 | semidirect |
| 84. C4×#595 | C24 | semidirect |
| 86. #63243 | C24 | semidirect |
| 90. C23×C17 | #104 | semidirect |
| 99. D4×C17 | C23×C4 | semidirect |
| 115. Dic34 | C23×C4 | semidirect |
| 123. C22×C17 | C2×#104 | semidirect |
| 141. C23×D4 | #595 | semidirect |
| 152. C2×C17 | C22×#104 | semidirect |
| 168. C22×D4 | C2×#595 | semidirect |
| 186. C17 | C23×#104 | semidirect |
| 203. C2×D4 | C22×#595 | semidirect |
| 229. C23 | #10587548 | direct (N × H) |
| 236. D4 | C23×#595 | semidirect |
| 258. C22 | C2×#10587548 | direct (N × H) |
| 269. C2 | C22×#10587548 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#63243 | 2 |
| C23×C4×#595 | 2 |
| C22×#10587548 | 2 |
| C23×#63254 | 2 |
| C23×#104 | 17 |