Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
738 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 173 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. C2×#11745304 | C2 | semidirect |
| 3. #14271319 | C2 | semidirect |
| 4. #14271302 | C2 | semidirect |
| 5. #14271172 | C2 | semidirect |
| 6. #14271127 | C2 | semidirect |
| 7. C23×Q8×C29 | C2 | semidirect |
| 17. C2×#90785 | C22 | semidirect |
| 19. C2×#90784 | C22 | semidirect |
| 26. #11745183 | C22 | semidirect |
| 35. C2×Q8×C29 | D4 | semidirect |
| 94. C22×C29 | #137 | semidirect |
| 104. C23×Q8 | D29 | semidirect |
| 136. C29 | #3004 | semidirect |
| 146. C2×Q8 | C22⋊D29 | semidirect |
| 203. C22 | #11745304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745304 | 2 |
| #14271674 | 2 |
| #14271319 | 2 |
| #14271302 | 2 |
| #14271172 | 2 |
| #14271127 | 2 |
| C23×Q8×C29 | 2 |
| #3004 | 29 |