Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
592 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. C2×#11745164 | C2 | semidirect |
| 3. C2×#11745183 | C2 | semidirect |
| 4. C2×#11745158 | C2 | semidirect |
| 7. C2×C29×#103 | C2 | semidirect |
| 14. C2×Q8×D29 | C4 | semidirect |
| 87. Q8×C29 | C22⋊C4 | semidirect |
| 118. Dic58 | C22⋊C4 | semidirect |
| 135. C2×D29 | #103 | semidirect |
| 149. C2×#103 | D29 | semidirect |
| 182. C29 | #1787 | semidirect |
| 245. Q8 | #90781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D29 | 2 |
| C2×#11745164 | 2 |
| C2×#11745183 | 2 |
| C2×#11745158 | 2 |
| C2×#11745168 | 2 |
| #14271020 | 2 |
| C2×C29×#103 | 2 |
| #1787 | 29 |