Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 170 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. #14272197 | C2 | semidirect |
| 3. #14272191 | C2 | semidirect |
| 4. #14272167 | C2 | semidirect |
| 5. #14272138 | C2 | semidirect |
| 6. C4×D29⋊C8 | C2 | semidirect |
| 42. D29⋊C8 | D4 | semidirect |
| 76. C4×C29 | #131 | semidirect |
| 108. C29 | #2931 | semidirect |
| 162. C4 | #11745348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745348 | 2 |
| #14272197 | 2 |
| #14272191 | 2 |
| #14272167 | 2 |
| #14272138 | 2 |
| C4×D29⋊C8 | 2 |
| #14271714 | 2 |
| #2931 | 29 |