Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
480 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 170 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. #14272203 | C2 | direct (N × H) |
| 15. C2×Q16×C29 | C4 | semidirect |
| 16. C2×#90785 | C4 | semidirect |
| 17. Q16×D29 | C4 | semidirect |
| 19. C2×Dic116 | C4 | semidirect |
| 44. Q16×C29 | C2×C4 | semidirect |
| 46. #90785 | C2×C4 | semidirect |
| 48. Dic116 | C2×C4 | semidirect |
| 94. C2×C29 | #441 | semidirect |
| 96. D29 | #441 | semidirect |
| 103. C2×Q16 | #1181 | semidirect |
| 115. C29 | C2×#441 | semidirect |
| 129. Q16 | C2×#1181 | semidirect |
| 181. C2 | #14272203 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#1181 | 2 |
| #14272203 | 2 |
| C2×#11745209 | 2 |
| C2×#11745225 | 2 |
| C2×#11745208 | 2 |
| C2×Q16×D29 | 2 |
| C2×#441 | 29 |