Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
568 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 2. #22577342 | C2 | semidirect |
| 3. #22577329 | C2 | semidirect |
| 5. #22577314 | C2 | semidirect |
| 6. C4×#14555487 | C2 | semidirect |
| 7. #22577249 | C2 | semidirect |
| 8. C2×C4×Q8×C137 | C2 | semidirect |
| 96. C137 | #2398 | semidirect |
| 98. C2×C4×Q8 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D548 | 2 |
| #22577342 | 2 |
| #22577329 | 2 |
| #22577320 | 2 |
| #22577314 | 2 |
| C4×#14555487 | 2 |
| #22577249 | 2 |
| C2×C4×Q8×C137 | 2 |
| #2398 | 137 |