Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1488 conjugacy classes of subgroups; only the 762 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 762 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. #14272231 | C2 | direct (N × H) |
| 2. C2×Q8×#1181 | C2 | semidirect |
| 5. C22×Q8×C29 | C4 | semidirect |
| 6. C2×Q8×D29 | C4 | semidirect |
| 7. C2×Q8×D29 | C4 | semidirect |
| 11. C22×Dic58 | C4 | semidirect |
| 13. Q8×#1181 | C22 | semidirect |
| 20. C2×Q8×C29 | C2×C4 | semidirect |
| 24. Q8×D29 | C2×C4 | semidirect |
| 31. C2×Dic58 | C2×C4 | semidirect |
| 71. C2×C29 | #519 | semidirect |
| 74. D29 | #519 | semidirect |
| 81. C22×Q8 | #1181 | semidirect |
| 88. C29 | C2×#519 | semidirect |
| 96. C2×Q8 | C2×#1181 | semidirect |
| 141. C2 | #14272231 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272231 | 2 |
| C2×Q8×#1181 | 2 |
| C2×#11745345 | 2 |
| C22×Q8×D29 | 2 |
| C2×#519 | 29 |