Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
152 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 3. #14272088 | C2 | semidirect |
| 4. #14272087 | C2 | semidirect |
| 14. C29×M32 | C4 | semidirect |
| 15. #11745160 | C4 | semidirect |
| 17. C16×D29 | C4 | semidirect |
| 32. C16×C29 | C2×C4 | semidirect |
| 33. #90768 | C2×C4 | semidirect |
| 67. D29 | #365 | semidirect |
| 73. M32 | #1181 | semidirect |
| 80. C29 | C2×#365 | semidirect |
| 96. C16 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D29⋊#108 | 2 |
| C2×#11745209 | 2 |
| #14272088 | 2 |
| #14272087 | 2 |
| M32×D29 | 2 |
| C2×#365 | 29 |