Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 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. #22577753 | C2 | semidirect |
| 4. #22577710 | C2 | semidirect |
| 7. #22577610 | C2 | semidirect |
| 8. Q8×#11764040 | C2 | semidirect |
| 9. C4×#14555500 | C2 | semidirect |
| 115. C137 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578131 | 2 |
| #22577757 | 2 |
| #22577753 | 2 |
| #22577710 | 2 |
| #22577683 | 2 |
| #22577622 | 2 |
| #22577610 | 2 |
| Q8×#11764040 | 2 |
| C4×#14555500 | 2 |
| C4×#14555498 | 2 |
| #556×C137 | 2 |
| #3364 | 137 |