Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
372 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 94 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. D29⋊(C4⋊C8) | C2 | semidirect |
| 3. #14272109 | C2 | semidirect |
| 4. #14272036 | C2 | semidirect |
| 12. C4×D4×C29 | C4 | semidirect |
| 13. D4×Dic29 | C4 | semidirect |
| 15. #11745255 | C4 | semidirect |
| 19. C4×D116 | C4 | semidirect |
| 74. D4×C29 | C4⋊C4 | semidirect |
| 88. D116 | C4⋊C4 | semidirect |
| 123. C4×C29 | #102 | semidirect |
| 128. Dic29 | #102 | semidirect |
| 153. C4×D4 | #1181 | semidirect |
| 163. C29 | #1802 | semidirect |
| 215. D4 | C4⋊#1181 | semidirect |
| 267. C4 | #11745223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D29⋊(C4⋊C8) | 2 |
| C2×#11745223 | 2 |
| #14272109 | 2 |
| #14272036 | 2 |
| C4×D4×D29 | 2 |
| #1802 | 29 |