Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
592 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 298 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. #22578368 | C2 | direct (N × H) |
| 4. C2×#17984143 | C2 | semidirect |
| 5. C2×C4×#11764047 | C2 | semidirect |
| 7. C2×#14555520 | C4 | semidirect |
| 9. C2×#14555518 | C4 | semidirect |
| 14. #17984143 | C22 | semidirect |
| 15. C4×#11764047 | C22 | semidirect |
| 23. #14555520 | C2×C4 | semidirect |
| 24. #14555518 | C2×C4 | semidirect |
| 80. C2×C137 | #405 | semidirect |
| 85. C137 | C2×#405 | semidirect |
| 167. C2 | #22578368 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555520 | 2 |
| C22×#14555518 | 2 |
| #22578368 | 2 |
| C2×#17984143 | 2 |
| C2×C4×#11764047 | 2 |
| C2×#17984046 | 2 |
| C2×#405 | 137 |