Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
616 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 253 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. C22×C8×D29 | C2 | semidirect |
| 3. #14271228 | C2 | direct (N × H) |
| 4. C2×#11745168 | C2 | semidirect |
| 5. C2×C4×#6597 | C2 | semidirect |
| 6. C2×C29×C4⋊C8 | C2 | semidirect |
| 16. C2×C8×D29 | C22 | semidirect |
| 19. C29×C4⋊C8 | C22 | semidirect |
| 20. #11745168 | C22 | semidirect |
| 21. C4×#6597 | C22 | semidirect |
| 27. C2×D116 | C8 | semidirect |
| 40. C2×#6597 | D4 | semidirect |
| 47. C22×D29 | C2×C8 | semidirect |
| 50. C2×C4×C29 | C2×C8 | semidirect |
| 59. D116 | C2×C8 | semidirect |
| 65. #6597 | C2×D4 | semidirect |
| 74. C2×D29 | C22×C8 | semidirect |
| 77. C4×C29 | C22×C8 | semidirect |
| 84. C2×C4⋊C8 | D29 | semidirect |
| 87. C2×C29 | C8×D4 | semidirect |
| 104. C4⋊C8 | C2×D29 | semidirect |
| 107. C29 | C2×C8×D4 | semidirect |
| 142. C2×C4 | C8×D29 | semidirect |
| 163. C4 | C2×C8×D29 | semidirect |
| 167. C2 | #14271228 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D29 | 2 |
| C2×C4×D116 | 2 |
| #14271228 | 2 |
| C2×#11745168 | 2 |
| C2×C4×#6597 | 2 |
| C2×C29×C4⋊C8 | 2 |
| C2×C8×D4 | 29 |