Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 166 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×#11745348 | C2 | semidirect |
| 2. C2×#11745346 | C2 | semidirect |
| 3. #14272196 | C2 | semidirect |
| 4. #14272190 | C2 | semidirect |
| 5. #14272168 | C2 | semidirect |
| 6. #14272138 | C2 | semidirect |
| 7. #14272137 | C2 | semidirect |
| 8. C4×D29⋊C8 | C2 | semidirect |
| 61. D29⋊C8 | D4 | semidirect |
| 108. Dic29 | #131 | semidirect |
| 149. C29 | #2931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745348 | 2 |
| C2×#11745346 | 2 |
| #14272196 | 2 |
| #14272190 | 2 |
| #14272168 | 2 |
| #14272138 | 2 |
| #14272137 | 2 |
| C4×D29⋊C8 | 2 |
| #14271712 | 2 |
| #2931 | 29 |