Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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. #22577785 | C2 | semidirect |
| 4. #22577782 | C2 | semidirect |
| 5. #22577779 | C2 | semidirect |
| 6. #22577777 | C2 | semidirect |
| 7. #22577775 | C2 | semidirect |
| 8. C2×C4×#11764040 | C2 | semidirect |
| 9. #532×C137 | C2 | semidirect |
| 42. C2×#11764040 | D4 | semidirect |
| 93. C4×C137 | #135 | semidirect |
| 101. C137 | #3147 | semidirect |
| 105. #532 | D137 | semidirect |
| 196. C4 | #17984108 | 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 |
| #22577785 | 2 |
| #22577782 | 2 |
| #22577779 | 2 |
| #22577777 | 2 |
| #22577775 | 2 |
| C2×C4×#11764040 | 2 |
| #532×C137 | 2 |
| #3147 | 137 |