Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
872 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 214 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. C2×Q8×#1181 | C2 | semidirect |
| 2. #14272115 | C2 | semidirect |
| 3. #14272105 | C2 | semidirect |
| 4. C4×C22⋊#1181 | C2 | semidirect |
| 6. C2×#41×C29 | C4 | semidirect |
| 8. C2×#90809 | C4 | semidirect |
| 10. C2×#90807 | C4 | semidirect |
| 12. C2×#90805 | C4 | semidirect |
| 58. C2×#1181 | #41 | semidirect |
| 59. Q8×C29 | C22⋊C4 | semidirect |
| 73. Dic58 | C22⋊C4 | semidirect |
| 110. C2×#41 | #1181 | semidirect |
| 121. C29 | #2341 | semidirect |
| 155. Q8 | C22⋊#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#1181 | 2 |
| #14272115 | 2 |
| #14272105 | 2 |
| C4×C22⋊#1181 | 2 |
| C2×#41×D29 | 2 |
| #2341 | 29 |