Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
438 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 80 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×D4×#1181 | C2 | semidirect |
| 2. C2×#11745223 | C2 | semidirect |
| 3. C2×#11745223 | C2 | semidirect |
| 4. #14272115 | C2 | semidirect |
| 5. #14272037 | C2 | semidirect |
| 6. (C2×#1181)⋊C8 | C2 | semidirect |
| 20. C2×D8×C29 | C4 | semidirect |
| 21. C2×#90782 | C4 | semidirect |
| 22. C2×#90782 | C4 | semidirect |
| 25. C2×D232 | C4 | semidirect |
| 39. C2×D4×C29 | C2×C4 | semidirect |
| 51. C2×D116 | C2×C4 | semidirect |
| 66. C2×C8×C29 | C2×C4 | semidirect |
| 69. C2×#6597 | C2×C4 | semidirect |
| 102. C2×#1181 | D8 | semidirect |
| 106. D4×C29 | C22⋊C4 | semidirect |
| 116. D116 | C22⋊C4 | semidirect |
| 186. C2×D8 | #1181 | semidirect |
| 199. C29 | #1879 | semidirect |
| 215. C2×D4 | C2×#1181 | semidirect |
| 234. C2×C8 | C2×#1181 | semidirect |
| 272. D4 | C22⋊#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#1181 | 2 |
| C2×#11745223 | 2 |
| #14272115 | 2 |
| #14272037 | 2 |
| (C2×#1181)⋊C8 | 2 |
| C2×D8×D29 | 2 |
| #1879 | 29 |