Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1072 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 306 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×D29⋊C8 | C2 | semidirect |
| 2. C2×#11745219 | C2 | semidirect |
| 3. D29⋊(C22⋊C8) | C2 | direct (N × H) |
| 4. C2×C22⋊#6599 | C2 | semidirect |
| 16. C22×#6599 | C22 | semidirect |
| 18. C2×D29⋊C8 | C22 | semidirect |
| 19. C22⋊#6599 | C22 | semidirect |
| 20. #11745219 | C22 | semidirect |
| 24. C23×D29 | C8 | semidirect |
| 50. C2×#6599 | C23 | semidirect |
| 54. C23×C29 | C2×C8 | semidirect |
| 64. C22×D29 | C2×C8 | semidirect |
| 65. C22×D29 | C2×C8 | semidirect |
| 94. C22×C29 | C22×C8 | semidirect |
| 101. C2×D29 | C22⋊C8 | semidirect |
| 104. C2×D29 | C22×C8 | semidirect |
| 117. C2×C29 | C2×C22⋊C8 | semidirect |
| 122. D29 | C2×C22⋊C8 | semidirect |
| 138. C29 | C22×C22⋊C8 | semidirect |
| 184. C23 | D29⋊C8 | semidirect |
| 219. C22 | C2×D29⋊C8 | semidirect |
| 231. C2 | D29⋊(C22⋊C8) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D29⋊C8 | 2 |
| C2×#11745219 | 2 |
| D29⋊(C22⋊C8) | 2 |
| C2×C22⋊#6599 | 2 |
| C23×C4×D29 | 2 |
| C22×C22⋊C8 | 29 |