Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
362 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 103 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×#11924467 | C2 | semidirect |
| 5. #14557295 | C2 | semidirect |
| 6. #14557288 | C2 | semidirect |
| 7. C37×#389 | C2 | semidirect |
| 18. #11924456 | C4 | semidirect |
| 44. C4⋊C4×C37 | C2×C4 | semidirect |
| 55. C2×#64436 | C2×C4 | semidirect |
| 88. D148 | C4⋊C4 | semidirect |
| 128. #389 | D37 | semidirect |
| 131. C37 | #1864 | semidirect |
| 176. C4⋊C4 | C4×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D148 | 2 |
| C2×#11924467 | 2 |
| C2×#11924456 | 2 |
| #14557295 | 2 |
| #14557288 | 2 |
| C37×#389 | 2 |
| #1864 | 37 |