Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#17984108 | C2 | semidirect |
| 2. #22577953 | C2 | semidirect |
| 3. #22577798 | C2 | semidirect |
| 4. #22577795 | C2 | semidirect |
| 5. #22577793 | C2 | semidirect |
| 6. #22577790 | C2 | semidirect |
| 7. C2×#17983999 | C2 | semidirect |
| 8. #532×C137 | C2 | semidirect |
| 40. C2×#11764040 | D4 | semidirect |
| 97. C137 | #3150 | semidirect |
| 101. #532 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984108 | 2 |
| #22577953 | 2 |
| #22577798 | 2 |
| #22577795 | 2 |
| #22577793 | 2 |
| #22577790 | 2 |
| C2×#17983999 | 2 |
| #532×C137 | 2 |
| #3150 | 137 |