Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
164 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 64 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×#11745206 | C2 | semidirect |
| 2. C2×D29⋊C16 | C2 | semidirect |
| 3. C4⋊#90770 | C2 | semidirect |
| 4. #14272058 | C2 | semidirect |
| 5. #14272058 | C2 | semidirect |
| 6. #14272051 | C2 | semidirect |
| 39. #90770 | D4 | semidirect |
| 64. C2×D29 | M32 | semidirect |
| 96. C29 | #2168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745206 | 2 |
| C2×D29⋊C16 | 2 |
| C4⋊#90770 | 2 |
| #14272058 | 2 |
| #14272051 | 2 |
| #14271228 | 2 |
| #2168 | 29 |