Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
476 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 253 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. #22577446 | C2 | semidirect |
| 4. #22577443 | C2 | semidirect |
| 5. #22577439 | C2 | semidirect |
| 6. C2×#17984021 | C2 | semidirect |
| 8. #17984095 | C4 | semidirect |
| 26. #14555494 | C2×C4 | semidirect |
| 27. C2×#11764040 | C2×C4 | semidirect |
| 76. C137 | #2913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984095 | 2 |
| #22577886 | 2 |
| #22577446 | 2 |
| #22577443 | 2 |
| #22577439 | 2 |
| C2×#17984021 | 2 |
| #520×C137 | 2 |
| #2913 | 137 |