Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
336 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C2×#11745208 | C2 | semidirect |
| 4. C2×C8×#1181 | C2 | semidirect |
| 5. (C2×#1181)⋊C8 | C2 | semidirect |
| 6. (C2×#1181)⋊C8 | C2 | semidirect |
| 19. C22⋊#6599 | C4 | semidirect |
| 20. #11745219 | C4 | semidirect |
| 23. C29×C22⋊C8 | C4 | semidirect |
| 24. C22⋊#6597 | C4 | semidirect |
| 25. #11745168 | C4 | semidirect |
| 26. #11745168 | C4 | semidirect |
| 149. C22⋊C8 | #1181 | semidirect |
| 152. C29 | #1750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745345 | 2 |
| D29⋊(C22⋊C8) | 2 |
| C2×#11745208 | 2 |
| C2×C8×#1181 | 2 |
| (C2×#1181)⋊C8 | 2 |
| C22⋊C8×D29 | 2 |
| #1750 | 29 |