Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14271604 | C2 | direct (N × H) |
| 3. C2×#11745177 | C2 | semidirect |
| 4. C2×#11745176 | C2 | semidirect |
| 5. C2×#11745160 | C2 | semidirect |
| 6. C22×Q16×C29 | C2 | semidirect |
| 12. C2×Q16×C29 | C22 | semidirect |
| 19. #11745177 | C22 | semidirect |
| 20. #11745176 | C22 | semidirect |
| 21. #11745160 | C22 | semidirect |
| 81. C22×Q16 | D29 | semidirect |
| 87. C2×C29 | #510 | semidirect |
| 98. C2×Q16 | C2×D29 | semidirect |
| 106. C29 | C2×#510 | semidirect |
| 165. C2 | #14271604 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745266 | 2 |
| #14271604 | 2 |
| C2×#11745177 | 2 |
| C2×#11745176 | 2 |
| C2×#11745160 | 2 |
| C22×Q16×C29 | 2 |
| C2×#510 | 29 |