Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C2×#17984111 | C2 | semidirect |
| 2. C2×#17984109 | C2 | semidirect |
| 3. C2×#17984107 | C2 | semidirect |
| 4. #22577952 | C2 | semidirect |
| 5. #22577787 | C2 | semidirect |
| 6. #22577785 | C2 | semidirect |
| 7. #22577781 | C2 | semidirect |
| 8. #22577778 | C2 | semidirect |
| 9. #22577774 | C2 | semidirect |
| 10. C4×C8×D137 | C2 | semidirect |
| 11. #495×C137 | C2 | semidirect |
| 62. C8×D137 | D4 | semidirect |
| 63. C8×D137 | D4 | semidirect |
| 119. Dic137 | #135 | semidirect |
| 125. C137 | #3147 | semidirect |
| 133. #495 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984111 | 2 |
| C2×#17984109 | 2 |
| C2×#17984107 | 2 |
| #22577952 | 2 |
| #22577787 | 2 |
| #22577785 | 2 |
| #22577781 | 2 |
| #22577778 | 2 |
| #22577774 | 2 |
| C4×C8×D137 | 2 |
| #495×C137 | 2 |
| #3147 | 137 |