Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
552 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 165 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. #14271543 | C2 | semidirect |
| 4. #14271542 | C2 | semidirect |
| 5. #14271541 | C2 | semidirect |
| 7. C29×#494 | C2 | semidirect |
| 51. C4×D29 | Q16 | semidirect |
| 62. C4×C29 | C2×Q16 | semidirect |
| 66. Dic29 | C2×Q16 | semidirect |
| 72. #494 | D29 | direct (N × H) |
| 76. D29 | #494 | direct (N × H) |
| 92. C29 | C2×#494 | semidirect |
| 134. C4 | Q16×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D29 | 2 |
| C4⋊Q8×D29 | 2 |
| #14271543 | 2 |
| #14271542 | 2 |
| #14271541 | 2 |
| C4×C8×D29 | 2 |
| C29×#494 | 2 |
| C2×#494 | 29 |