Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
542 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22561199 | C2 | semidirect |
| 3. #22558965 | C2 | semidirect |
| 4. #22558890 | C2 | semidirect |
| 6. C8×#11761612 | C2 | semidirect |
| 64. #11761612 | SD16 | semidirect |
| 127. C8×C67 | #100 | semidirect |
| 161. C67 | #9793 | semidirect |
| 285. C8 | #14523960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561199 | 2 |
| #22561050 | 2 |
| #22558965 | 2 |
| #22558890 | 2 |
| #22558877 | 2 |
| C8×#11761612 | 2 |
| C2×#492×C67 | 2 |
| #9793 | 67 |