Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
436 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 125 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. C4⋊Q8×D29 | C2 | semidirect |
| 3. #14271525 | C2 | semidirect |
| 4. #14271524 | C2 | semidirect |
| 5. #14271523 | C2 | semidirect |
| 6. #14271522 | C2 | semidirect |
| 7. #14271521 | C2 | semidirect |
| 8. #103×D29 | C2 | semidirect |
| 10. #97×D29 | C2 | semidirect |
| 11. C29×#489 | C2 | semidirect |
| 15. C29×C4⋊Q8 | C22 | semidirect |
| 24. #11745250 | C22 | semidirect |
| 31. #11745231 | C22 | semidirect |
| 32. C29×#103 | C22 | semidirect |
| 34. C29×#97 | C22 | semidirect |
| 35. #11745183 | C22 | semidirect |
| 38. #11745164 | C22 | semidirect |
| 39. #11745163 | C22 | semidirect |
| 40. #11745158 | C22 | semidirect |
| 42. #11745151 | C22 | semidirect |
| 143. #489 | D29 | direct (N × H) |
| 152. D29 | #489 | direct (N × H) |
| 161. C4⋊Q8 | C2×D29 | semidirect |
| 176. #103 | C2×D29 | semidirect |
| 183. #97 | C2×D29 | semidirect |
| 184. C29 | C2×#489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D29 | 2 |
| #124×D29 | 2 |
| #14271525 | 2 |
| #14271524 | 2 |
| #14271523 | 2 |
| #14271522 | 2 |
| #14271521 | 2 |
| #103×D29 | 2 |
| #102×D29 | 2 |
| #97×D29 | 2 |
| C29×#489 | 2 |
| C2×#489 | 29 |