Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1072 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 349 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. C23×#6597 | C2 | semidirect |
| 3. C2×#11745157 | C2 | direct (N × H) |
| 4. C22×C4⋊C4×C29 | C2 | semidirect |
| 10. C22×D116 | C4 | semidirect |
| 13. C2×C4⋊C4×C29 | C22 | semidirect |
| 15. C22×#6597 | C22 | semidirect |
| 16. #11745157 | C22 | direct (N × H) |
| 31. C2×D116 | C2×C4 | semidirect |
| 34. C4⋊C4×C29 | C23 | semidirect |
| 36. C2×#6597 | C23 | semidirect |
| 55. D116 | C22×C4 | semidirect |
| 58. C22×C29 | #102 | semidirect |
| 73. C22×C4⋊C4 | D29 | semidirect |
| 75. C2×C29 | C2×#102 | semidirect |
| 90. C2×C4⋊C4 | C2×D29 | semidirect |
| 92. C29 | C22×#102 | semidirect |
| 112. C4⋊C4 | C22×D29 | semidirect |
| 137. C22 | #11745157 | direct (N × H) |
| 147. C2 | C2×#11745157 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D116 | 2 |
| C23×#6597 | 2 |
| C2×#11745157 | 2 |
| C22×C4⋊C4×C29 | 2 |
| C22×#102 | 29 |