Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
612 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 94 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×#11745225 | C2 | semidirect |
| 2. C2×#11745223 | C2 | semidirect |
| 3. D29⋊(C22⋊C8) | C2 | semidirect |
| 4. #14272105 | C2 | semidirect |
| 6. C2×#41×C29 | C4 | semidirect |
| 9. C2×#90809 | C4 | semidirect |
| 12. C2×#90807 | C4 | semidirect |
| 16. C2×#90805 | C4 | semidirect |
| 92. Q8×C29 | C22⋊C4 | semidirect |
| 95. D4×C29 | C22⋊C4 | semidirect |
| 112. D116 | C22⋊C4 | semidirect |
| 124. Dic58 | C22⋊C4 | semidirect |
| 177. C2×#41 | #1181 | semidirect |
| 191. C29 | #1788 | semidirect |
| 257. Q8 | C22⋊#1181 | semidirect |
| 266. D4 | C22⋊#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745225 | 2 |
| C2×#11745223 | 2 |
| D29⋊(C22⋊C8) | 2 |
| #14272105 | 2 |
| C2×#41×D29 | 2 |
| #1788 | 29 |