Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22578131 | C2 | semidirect |
| 3. #22577755 | C2 | semidirect |
| 4. #22577752 | C2 | semidirect |
| 5. #22577687 | C2 | semidirect |
| 8. #22577527 | C2 | semidirect |
| 11. #475×C137 | C2 | semidirect |
| 78. Dic274 | SD16 | semidirect |
| 118. C137 | #3359 | semidirect |
| 125. #475 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578131 | 2 |
| #22578068 | 2 |
| #22577755 | 2 |
| #22577752 | 2 |
| #22577687 | 2 |
| #22577609 | 2 |
| #22577607 | 2 |
| #22577527 | 2 |
| C4×#14555497 | 2 |
| #22577490 | 2 |
| #475×C137 | 2 |
| #3359 | 137 |