Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
432 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 110 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×#6599 | C2 | semidirect |
| 2. C2×#11745219 | C2 | semidirect |
| 3. C2×C22⋊#6599 | C2 | semidirect |
| 4. #14272029 | C2 | semidirect |
| 27. C2×C22⋊D29 | C8 | semidirect |
| 45. C2×#6599 | D4 | semidirect |
| 61. C22×D29 | C2×C8 | semidirect |
| 74. C2×Dic29 | C2×C8 | semidirect |
| 89. C22×C29 | C22⋊C8 | semidirect |
| 134. C29 | #1869 | semidirect |
| 207. C22 | #11745219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#6599 | 2 |
| C2×#11745219 | 2 |
| C2×C22⋊#6599 | 2 |
| #14272029 | 2 |
| C2×#11745243 | 2 |
| #1869 | 29 |