Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22559015 | C2 | semidirect |
| 4. #22558282 | C2 | semidirect |
| 5. #22558174 | C2 | semidirect |
| 6. #22558128 | C2 | semidirect |
| 46. Dic268 | M16 | semidirect |
| 88. C67⋊C8 | SD32 | semidirect |
| 113. C67 | #12071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523987 | 2 |
| #22559094 | 2 |
| #22559015 | 2 |
| #22558282 | 2 |
| #22558174 | 2 |
| #22558128 | 2 |
| C67×#1331 | 2 |
| #12071 | 67 |