Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
568 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 228 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 |
|---|---|---|
| 13. C4×Q8×C29 | C4 | semidirect |
| 14. Q8×Dic29 | C4 | semidirect |
| 16. #11745249 | C4 | semidirect |
| 18. C4×Dic58 | C4 | semidirect |
| 32. C4⋊#1181 | Q8 | direct (N × H) |
| 48. Q8×C29 | C4⋊C4 | semidirect |
| 61. Dic58 | C4⋊C4 | semidirect |
| 74. C4×C29 | C4×Q8 | semidirect |
| 77. Dic29 | C4×Q8 | semidirect |
| 95. C4×Q8 | #1181 | semidirect |
| 104. C29 | Q8×C4⋊C4 | semidirect |
| 128. Q8 | C4⋊#1181 | direct (N × H) |
| 161. 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 |
| #14272114 | 2 |
| #14272109 | 2 |
| C4×C4⋊#1181 | 2 |
| C4×Q8×D29 | 2 |
| Q8×C4⋊C4 | 29 |