Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
592 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
| 5. C22×Q8×C29 | C4 | semidirect |
| 9. C2×Q8×D29 | C4 | semidirect |
| 14. C22×Dic58 | C4 | semidirect |
| 67. Q8×C29 | C22⋊C4 | semidirect |
| 88. Dic58 | C22⋊C4 | semidirect |
| 93. C22×C29 | #103 | semidirect |
| 99. C2×D29 | #103 | semidirect |
| 129. C22×Q8 | #1181 | semidirect |
| 139. C29 | #1787 | semidirect |
| 187. Q8 | C22⋊#1181 | semidirect |
| 219. C22 | #11745225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745225 | 2 |
| D29⋊(C22⋊C8) | 2 |
| #14272105 | 2 |
| C22×Q8×D29 | 2 |
| #1787 | 29 |