Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
320 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 53 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. #14271313 | C2 | semidirect |
| 2. #14271296 | C2 | semidirect |
| 3. #14271072 | C2 | semidirect |
| 4. #14270900 | C2 | semidirect |
| 5. #14270897 | C2 | semidirect |
| 6. #14270887 | C2 | semidirect |
| 7. C29×#538 | C2 | semidirect |
| 29. C2×Q8×C29 | D4 | semidirect |
| 33. C2×D4×C29 | D4 | semidirect |
| 46. C4⋊C4×C29 | D4 | semidirect |
| 47. C4⋊C4×C29 | D4 | semidirect |
| 128. #538 | D29 | semidirect |
| 162. C29 | #1600 | semidirect |
| 165. C2×Q8 | C22⋊D29 | semidirect |
| 175. C2×D4 | C22⋊D29 | semidirect |
| 186. C4⋊C4 | C22⋊D29 | semidirect |
| 187. C4⋊C4 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271313 | 2 |
| #14271296 | 2 |
| #14271072 | 2 |
| #14270900 | 2 |
| #14270897 | 2 |
| #14270887 | 2 |
| C29×#538 | 2 |
| #1600 | 29 |