Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
588 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 210 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 |
|---|---|---|
| 18. C29×C4⋊Q8 | C4 | semidirect |
| 19. #11745306 | C4 | semidirect |
| 21. #11745250 | C4 | semidirect |
| 23. #11745231 | C4 | semidirect |
| 44. C4×#1181 | Q8 | semidirect |
| 85. #1181 | C4⋊Q8 | direct (N × H) |
| 88. C4×C29 | C4×Q8 | semidirect |
| 91. Dic29 | C4×Q8 | semidirect |
| 108. C4⋊Q8 | #1181 | direct (N × H) |
| 121. C29 | C4×C4⋊Q8 | semidirect |
| 187. C4 | Q8×#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×#1181)⋊Q8 | 2 |
| #14272114 | 2 |
| #14272109 | 2 |
| C4⋊C4×#1181 | 2 |
| C42×#1181 | 2 |
| C4⋊Q8×D29 | 2 |
| C4×C4⋊Q8 | 29 |