Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
500 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 166 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. C2×#17984176 | C2 | semidirect |
| 2. C2×#17984175 | C2 | semidirect |
| 3. #22578436 | C2 | semidirect |
| 4. #22578430 | C2 | semidirect |
| 5. #22578408 | C2 | semidirect |
| 6. #22578378 | C2 | semidirect |
| 7. #22578377 | C2 | semidirect |
| 8. C4×#14555518 | C2 | semidirect |
| 40. #14555518 | D4 | semidirect |
| 107. Dic137 | #131 | semidirect |
| 115. C137 | #2931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984176 | 2 |
| C2×#17984175 | 2 |
| #22578436 | 2 |
| #22578430 | 2 |
| #22578408 | 2 |
| #22578378 | 2 |
| #22578377 | 2 |
| C4×#14555518 | 2 |
| #22577952 | 2 |
| #2931 | 137 |