Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
348 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 102 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. C2×#11745208 | C2 | semidirect |
| 3. C2×C8×#1181 | C2 | semidirect |
| 5. (C2×#1181)⋊C8 | C2 | semidirect |
| 6. (C2×#1181)⋊C8 | C2 | semidirect |
| 10. C2×#90800 | C4 | semidirect |
| 15. C2×#90796 | C4 | semidirect |
| 23. C29×C22⋊C8 | C4 | semidirect |
| 24. C22⋊#6597 | C4 | semidirect |
| 25. #11745168 | C4 | semidirect |
| 26. #11745168 | C4 | semidirect |
| 73. C2×#1181 | M16 | semidirect |
| 93. #6599 | C22⋊C4 | semidirect |
| 149. C22⋊C8 | #1181 | semidirect |
| 153. C29 | #1753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D29⋊M16 | 2 |
| C2×#11745208 | 2 |
| C2×C8×#1181 | 2 |
| C4×C22⋊#1181 | 2 |
| (C2×#1181)⋊C8 | 2 |
| C22⋊C8×D29 | 2 |
| #1753 | 29 |