Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
398 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 160 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. #14272214 | C2 | semidirect |
| 2. #14272193 | C2 | semidirect |
| 3. #14272191 | C2 | semidirect |
| 4. #14272185 | C2 | semidirect |
| 5. #14272182 | C2 | semidirect |
| 6. #14272167 | C2 | semidirect |
| 7. D29⋊(C4⋊C8) | C2 | semidirect |
| 73. D116 | M16 | semidirect |
| 138. C29 | #2990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272214 | 2 |
| #14272193 | 2 |
| #14272191 | 2 |
| #14272185 | 2 |
| #14272182 | 2 |
| #14272167 | 2 |
| D29⋊(C4⋊C8) | 2 |
| C4×#90809 | 2 |
| #2990 | 29 |