Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 3. #14271533 | C2 | semidirect |
| 4. #14271532 | C2 | semidirect |
| 5. #14271531 | C2 | semidirect |
| 6. #14271530 | C2 | semidirect |
| 9. C29×#491 | C2 | semidirect |
| 91. #491 | D29 | direct (N × H) |
| 96. D29 | #491 | direct (N × H) |
| 118. C29 | C2×#491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D29 | 2 |
| #125×D29 | 2 |
| #14271533 | 2 |
| #14271532 | 2 |
| #14271531 | 2 |
| #14271530 | 2 |
| #103×D29 | 2 |
| #97×D29 | 2 |
| C29×#491 | 2 |
| C2×#491 | 29 |