Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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. #22578216 | C2 | semidirect |
| 2. #22577841 | C2 | semidirect |
| 3. C2×#17984031 | C2 | semidirect |
| 4. #22577674 | C2 | semidirect |
| 5. #22577209 | C2 | semidirect |
| 6. #22577188 | C2 | semidirect |
| 7. #362×C137 | C2 | semidirect |
| 90. C137 | #2193 | semidirect |
| 96. #362 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578216 | 2 |
| #22577841 | 2 |
| C2×#17984031 | 2 |
| #22577674 | 2 |
| #22577209 | 2 |
| #22577188 | 2 |
| #362×C137 | 2 |
| #2193 | 137 |