Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 460 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 |
|---|---|---|
| 3. #22577658 | C2 | semidirect |
| 4. #22577641 | C2 | semidirect |
| 5. #22577441 | C2 | semidirect |
| 6. #22577412 | C2 | semidirect |
| 7. C22×Q16×C137 | C2 | semidirect |
| 88. C137 | #3059 | semidirect |
| 90. C22×Q16 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984094 | 2 |
| #22577977 | 2 |
| #22577658 | 2 |
| #22577641 | 2 |
| #22577441 | 2 |
| #22577412 | 2 |
| C22×Q16×C137 | 2 |
| #3059 | 137 |