Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
792 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 197 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×#90784 | C2 | semidirect |
| 3. #14271302 | C2 | direct (N × H) |
| 4. C2×#11745183 | C2 | semidirect |
| 5. C2×C22⋊#6597 | C2 | semidirect |
| 6. C23×Q8×C29 | C2 | semidirect |
| 11. C22×Q8×C29 | C22 | semidirect |
| 17. C2×#90784 | C22 | semidirect |
| 23. #11745183 | C22 | semidirect |
| 24. C22⋊#6597 | C22 | semidirect |
| 33. C2×Q8×C29 | D4 | semidirect |
| 57. C23×C29 | SD16 | semidirect |
| 67. Q8×C29 | C2×D4 | semidirect |
| 90. C22×C29 | C2×SD16 | semidirect |
| 102. C23×Q8 | D29 | semidirect |
| 109. C2×C29 | #448 | semidirect |
| 118. C22×Q8 | C2×D29 | semidirect |
| 132. C29 | C2×#448 | semidirect |
| 141. C2×Q8 | C22⋊D29 | semidirect |
| 169. C23 | #90784 | semidirect |
| 175. Q8 | C2×C22⋊D29 | semidirect |
| 200. C22 | C2×#90784 | semidirect |
| 211. C2 | #14271302 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90784 | 2 |
| C2×#11745292 | 2 |
| #14271302 | 2 |
| C2×#11745183 | 2 |
| C2×C22⋊#6597 | 2 |
| C23×Q8×C29 | 2 |
| C2×#448 | 29 |