Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 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. #22578123 | C2 | semidirect |
| 3. #22577754 | C2 | semidirect |
| 4. #22577745 | C2 | semidirect |
| 5. #22577684 | C2 | semidirect |
| 6. #22577644 | C2 | semidirect |
| 7. #22577614 | C2 | semidirect |
| 8. #22577567 | C2 | semidirect |
| 9. C4×#14555499 | C2 | semidirect |
| 10. #22577400 | C2 | semidirect |
| 11. C8×D4×C137 | C2 | semidirect |
| 125. C137 | #3302 | semidirect |
| 136. C8×D4 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578123 | 2 |
| #22578058 | 2 |
| #22577754 | 2 |
| #22577745 | 2 |
| #22577684 | 2 |
| #22577644 | 2 |
| #22577614 | 2 |
| #22577567 | 2 |
| C4×#14555499 | 2 |
| #22577400 | 2 |
| C8×D4×C137 | 2 |
| #3302 | 137 |