Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
668 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 181 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×#90773 | C2 | semidirect |
| 2. C22×D232 | C2 | semidirect |
| 3. C2×#11745236 | C2 | semidirect |
| 4. C2×#11745237 | C2 | semidirect |
| 5. #14271552 | C2 | direct (N × H) |
| 6. C2×C29×#97 | C2 | semidirect |
| 15. C2×D232 | C22 | semidirect |
| 17. C2×#90773 | C22 | semidirect |
| 19. #11745237 | C22 | semidirect |
| 21. #11745236 | C22 | semidirect |
| 22. C29×#97 | C22 | semidirect |
| 40. C2×C8×C29 | D4 | semidirect |
| 69. C8×C29 | C2×D4 | semidirect |
| 89. C2×#97 | D29 | semidirect |
| 90. C2×C29 | #496 | semidirect |
| 110. #97 | C2×D29 | semidirect |
| 111. C29 | C2×#496 | semidirect |
| 131. C2×C8 | D116 | semidirect |
| 158. C8 | C2×D116 | semidirect |
| 174. C2 | #14271552 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90773 | 2 |
| C22×D232 | 2 |
| C2×#11745236 | 2 |
| C2×#11745237 | 2 |
| #14271552 | 2 |
| C2×C29×#97 | 2 |
| C2×#496 | 29 |