Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
792 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×Q8×D29 | C2 | semidirect |
| 2. C22×#90783 | C2 | semidirect |
| 4. #14271300 | C2 | direct (N × H) |
| 5. C2×#11745164 | C2 | semidirect |
| 6. C2×#11745183 | C2 | semidirect |
| 7. C2×#11745168 | C2 | semidirect |
| 8. C22×SD16×C29 | C2 | semidirect |
| 15. C2×Q8×D29 | C22 | semidirect |
| 21. C2×SD16×C29 | C22 | semidirect |
| 27. C2×#90783 | C22 | semidirect |
| 30. #11745183 | C22 | semidirect |
| 31. #11745168 | C22 | semidirect |
| 32. #11745164 | C22 | semidirect |
| 37. C2×Q8×C29 | D4 | semidirect |
| 63. C2×Dic58 | D4 | semidirect |
| 81. C22×D29 | SD16 | semidirect |
| 85. Q8×C29 | C2×D4 | semidirect |
| 109. Dic58 | C2×D4 | semidirect |
| 124. C2×D29 | C2×SD16 | semidirect |
| 134. C22×SD16 | D29 | semidirect |
| 141. C2×C29 | #448 | semidirect |
| 160. C2×SD16 | C2×D29 | semidirect |
| 170. C29 | C2×#448 | semidirect |
| 184. C2×Q8 | C22⋊D29 | semidirect |
| 227. Q8 | C2×C22⋊D29 | semidirect |
| 271. C2 | #14271300 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D29 | 2 |
| C22×#90783 | 2 |
| C2×#11745300 | 2 |
| #14271300 | 2 |
| C2×#11745164 | 2 |
| C2×#11745183 | 2 |
| C2×#11745168 | 2 |
| C22×SD16×C29 | 2 |
| C2×#448 | 29 |