Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 244 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. D4×#6599 | C2 | semidirect |
| 2. #14272179 | C2 | semidirect |
| 3. C2×C22⋊#6599 | C2 | semidirect |
| 7. C22×#6599 | C22 | semidirect |
| 14. C22⋊#6599 | C22 | semidirect |
| 15. C4⋊#6599 | C22 | semidirect |
| 16. C4×#6599 | C22 | semidirect |
| 18. C2×D4×C29 | C8 | semidirect |
| 35. C23×C29 | C2×C8 | semidirect |
| 38. D4×C29 | C2×C8 | semidirect |
| 39. C2×C4×C29 | C2×C8 | semidirect |
| 86. C29 | #2972 | semidirect |
| 88. C2×D4 | #6599 | semidirect |
| 105. C23 | C2×#6599 | semidirect |
| 108. D4 | C2×#6599 | semidirect |
| 118. C2×C4 | C2×#6599 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#6599 | 2 |
| #14272179 | 2 |
| C2×C22⋊#6599 | 2 |
| C2×D4×Dic29 | 2 |
| #2972 | 29 |