Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
298 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 23. C29×#103 | C4 | semidirect |
| 24. #11745183 | C4 | semidirect |
| 25. #11745164 | C4 | semidirect |
| 26. #11745158 | C4 | semidirect |
| 74. Q8×C29 | C4⋊C4 | semidirect |
| 92. Dic58 | C4⋊C4 | semidirect |
| 147. #103 | #1181 | semidirect |
| 149. C29 | #1865 | 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×#11745209 | 2 |
| C2×#11745225 | 2 |
| #14272114 | 2 |
| #14272036 | 2 |
| (C2×#1181)⋊C8 | 2 |
| #103×D29 | 2 |
| #1865 | 29 |