Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
384 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 3. #14271573 | C2 | semidirect |
| 4. #14271572 | C2 | semidirect |
| 5. #14271571 | C2 | semidirect |
| 6. #14271570 | C2 | semidirect |
| 7. #14271569 | C2 | semidirect |
| 11. C29×#501 | C2 | semidirect |
| 79. C8×D29 | Q8 | semidirect |
| 102. C8×C29 | C2×Q8 | semidirect |
| 103. #6597 | C2×Q8 | semidirect |
| 128. #501 | D29 | direct (N × H) |
| 135. D29 | #501 | direct (N × H) |
| 167. C29 | C2×#501 | semidirect |
| 228. C8 | Q8×D29 | 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 |
| #14271573 | 2 |
| #14271572 | 2 |
| #14271571 | 2 |
| #14271570 | 2 |
| #14271569 | 2 |
| #107×D29 | 2 |
| #106×D29 | 2 |
| #97×D29 | 2 |
| C29×#501 | 2 |
| C2×#501 | 29 |