Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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. C2×#11745270 | C2 | semidirect |
| 2. #14271730 | C2 | semidirect |
| 3. C2×#11745302 | C2 | semidirect |
| 4. C2×#11745173 | C2 | semidirect |
| 5. #14271169 | C2 | semidirect |
| 6. #14270924 | C2 | semidirect |
| 7. C2×C29×#100 | C2 | semidirect |
| 52. C2×D116 | D4 | semidirect |
| 53. C2×D116 | D4 | semidirect |
| 55. C2×Dic58 | D4 | semidirect |
| 59. M16×C29 | D4 | semidirect |
| 64. C4⋊Dic29 | D4 | semidirect |
| 67. C4×Dic29 | D4 | semidirect |
| 137. C2×#100 | D29 | semidirect |
| 167. C29 | #2002 | semidirect |
| 200. M16 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745270 | 2 |
| #14271730 | 2 |
| C2×#11745302 | 2 |
| C2×#11745173 | 2 |
| #14271169 | 2 |
| #14270924 | 2 |
| C2×C29×#100 | 2 |
| #2002 | 29 |