Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
480 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 146 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. (C2×#1181)⋊C8 | C2 | semidirect |
| 7. C2×#90800 | C4 | semidirect |
| 14. C2×#90796 | C4 | semidirect |
| 16. C2×M16×C29 | C4 | semidirect |
| 17. C2×#90777 | C4 | semidirect |
| 20. C2×#90772 | C4 | semidirect |
| 37. C2×#6599 | C2×C4 | semidirect |
| 45. C2×C8×C29 | C2×C4 | semidirect |
| 47. C2×#6597 | C2×C4 | semidirect |
| 60. C2×#1181 | M16 | semidirect |
| 120. C2×M16 | #1181 | semidirect |
| 127. C29 | #1728 | semidirect |
| 153. C2×C8 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D29⋊M16 | 2 |
| C22×C4×#1181 | 2 |
| (C2×#1181)⋊C8 | 2 |
| C2×M16×D29 | 2 |
| #1728 | 29 |