Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 189 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×#11745269 | C2 | semidirect |
| 3. #14271240 | C2 | semidirect |
| 4. #14271228 | C2 | semidirect |
| 5. #14271131 | C2 | semidirect |
| 6. C2×C4×#6597 | C2 | semidirect |
| 7. C29×#423 | C2 | semidirect |
| 42. C2×#6597 | D4 | semidirect |
| 76. C4×C29 | #131 | semidirect |
| 84. #423 | D29 | semidirect |
| 108. C29 | #2931 | semidirect |
| 160. C4 | #11745269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745269 | 2 |
| #14271713 | 2 |
| #14271240 | 2 |
| #14271228 | 2 |
| #14271131 | 2 |
| C2×C4×#6597 | 2 |
| C29×#423 | 2 |
| #2931 | 29 |