Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
336 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 93 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×#11745153 | C2 | semidirect |
| 3. C4×#90777 | C2 | semidirect |
| 4. C4×C4⋊C4×C29 | C2 | semidirect |
| 12. #11745237 | C4 | semidirect |
| 13. #11745236 | C4 | semidirect |
| 16. #11745231 | C4 | semidirect |
| 44. #90777 | D4 | semidirect |
| 83. C4×C29 | #104 | semidirect |
| 90. C4×C4⋊C4 | D29 | semidirect |
| 113. C29 | #1980 | semidirect |
| 176. C4 | #11745153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271713 | 2 |
| C2×#11745153 | 2 |
| C4×#90777 | 2 |
| C4×C4⋊C4×C29 | 2 |
| #1980 | 29 |