Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
360 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 114 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. C2×#17984143 | C2 | semidirect |
| 4. #22578269 | C2 | semidirect |
| 7. C2×#14555518 | C4 | semidirect |
| 11. #17984145 | C4 | semidirect |
| 40. #11764047 | C22⋊C4 | semidirect |
| 71. C2×D137 | #97 | semidirect |
| 84. C137 | #1752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555518 | 2 |
| C2×#17984145 | 2 |
| C2×#17984143 | 2 |
| #22578269 | 2 |
| #22577250 | 2 |
| #1752 | 137 |