Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
496 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 91 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. C22×#90782 | C2 | semidirect |
| 2. C2×#11745257 | C2 | semidirect |
| 3. C2×#11745300 | C2 | semidirect |
| 4. C2×#11745169 | C2 | semidirect |
| 5. C2×#11745168 | C2 | semidirect |
| 6. #14270925 | C2 | semidirect |
| 7. C2×C29×#102 | C2 | semidirect |
| 37. C2×D4×C29 | D4 | semidirect |
| 53. C2×D116 | D4 | semidirect |
| 64. C4⋊C4×C29 | D4 | semidirect |
| 69. C4⋊Dic29 | D4 | semidirect |
| 72. C2×#6597 | D4 | semidirect |
| 94. C22×D29 | D8 | semidirect |
| 166. C2×#102 | D29 | semidirect |
| 200. C29 | #1999 | semidirect |
| 221. C2×D4 | D116 | semidirect |
| 242. C4⋊C4 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90782 | 2 |
| C2×#11745257 | 2 |
| C2×#11745300 | 2 |
| C2×#11745169 | 2 |
| C2×#11745168 | 2 |
| #14270925 | 2 |
| C2×C29×#102 | 2 |
| #1999 | 29 |