Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
224 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. #22559107 | C2 | semidirect |
| 3. #22558282 | C2 | semidirect |
| 4. #22558172 | C2 | semidirect |
| 6. C8×C67⋊C16 | C2 | semidirect |
| 53. C67⋊C16 | M16 | semidirect |
| 85. C8×C67 | SD32 | semidirect |
| 113. C67 | #12082 | semidirect |
| 192. C8 | #14523987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523987 | 2 |
| #22559107 | 2 |
| #22558282 | 2 |
| #22558172 | 2 |
| #22558170 | 2 |
| C8×C67⋊C16 | 2 |
| C67×#1589 | 2 |
| #12082 | 67 |