Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
324 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 10. Q8×#1181 | C4 | semidirect |
| 20. #11745225 | C4 | semidirect |
| 23. C29×#103 | C4 | semidirect |
| 24. #11745183 | C4 | semidirect |
| 25. #11745164 | C4 | semidirect |
| 26. #11745158 | C4 | semidirect |
| 74. Q8×C29 | C42 | semidirect |
| 92. Dic58 | C42 | semidirect |
| 146. #103 | #1181 | semidirect |
| 149. C29 | #1763 | semidirect |
| 189. Q8 | C4×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#1181 | 2 |
| C2×#11745225 | 2 |
| C2×#11745208 | 2 |
| C4⋊C4×#1181 | 2 |
| #14272037 | 2 |
| #14272036 | 2 |
| #103×D29 | 2 |
| #1763 | 29 |