Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
412 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 162 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. #14272188 | C2 | semidirect |
| 2. #14272187 | C2 | semidirect |
| 3. D29⋊(C4⋊C8) | C2 | semidirect |
| 5. #14272122 | C2 | semidirect |
| 6. C4×D29⋊C8 | C2 | semidirect |
| 22. #11745220 | C22 | semidirect |
| 24. #11745218 | C22 | semidirect |
| 25. C4⋊#6599 | C22 | semidirect |
| 26. C4×#6599 | C22 | semidirect |
| 106. D29 | #433 | semidirect |
| 126. C29 | C2×#433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272188 | 2 |
| #14272187 | 2 |
| D29⋊(C4⋊C8) | 2 |
| D29⋊(C22⋊C8) | 2 |
| #14272122 | 2 |
| C4×D29⋊C8 | 2 |
| #117×D29 | 2 |
| C2×#433 | 29 |