Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 145 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. #14271565 | C2 | semidirect |
| 3. #14271564 | C2 | semidirect |
| 4. #14271563 | C2 | semidirect |
| 5. #14271562 | C2 | semidirect |
| 9. C29×#499 | C2 | semidirect |
| 79. #499 | D29 | direct (N × H) |
| 85. D29 | #499 | direct (N × H) |
| 105. C29 | C2×#499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×D29 | 2 |
| #14271565 | 2 |
| #14271564 | 2 |
| #14271563 | 2 |
| #14271562 | 2 |
| #107×D29 | 2 |
| #106×D29 | 2 |
| C4×C8×D29 | 2 |
| C29×#499 | 2 |
| C2×#499 | 29 |