Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
488 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 178 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. Q16×#1181 | 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 |
| 45. Q16×C29 | C2×C4 | semidirect |
| 47. #90785 | C2×C4 | semidirect |
| 49. Dic116 | C2×C4 | semidirect |
| 56. C2×#1181 | Q16 | direct (N × H) |
| 86. #1181 | C2×Q16 | direct (N × H) |
| 99. C2×C29 | C4×Q16 | semidirect |
| 101. D29 | C4×Q16 | semidirect |
| 109. C2×Q16 | #1181 | direct (N × H) |
| 121. C29 | C2×C4×Q16 | semidirect |
| 136. Q16 | C2×#1181 | direct (N × H) |
| 193. C2 | Q16×#1181 | 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 |
| Q16×#1181 | 2 |
| C2×#11745210 | 2 |
| C2×#11745225 | 2 |
| C2×C8×#1181 | 2 |
| C2×Q16×D29 | 2 |
| C2×C4×Q16 | 29 |