Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#11745309 | C2 | semidirect |
| 4. #14271548 | C2 | direct (N × H) |
| 5. C2×C8×Dic29 | C2 | semidirect |
| 6. C22×Q16×C29 | C2 | semidirect |
| 10. C2×Q16×C29 | C22 | semidirect |
| 13. #11745309 | C22 | semidirect |
| 15. C2×#90784 | C22 | semidirect |
| 21. C8×Dic29 | C22 | semidirect |
| 76. C22×Q16 | D29 | semidirect |
| 82. C2×C29 | #495 | semidirect |
| 89. C2×Q16 | C2×D29 | semidirect |
| 101. C29 | C2×#495 | semidirect |
| 156. C2 | #14271548 | 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 |
| C22×D232 | 2 |
| C2×#11745309 | 2 |
| #14271548 | 2 |
| C2×C8×Dic29 | 2 |
| C22×Q16×C29 | 2 |
| C2×#495 | 29 |