Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22562010 | C2 | semidirect |
| 3. #22558963 | C2 | semidirect |
| 4. #22558180 | C2 | semidirect |
| 5. #22558178 | C2 | semidirect |
| 6. #22558176 | C2 | semidirect |
| 7. C67×#1333 | C2 | semidirect |
| 72. Dic268 | M16 | semidirect |
| 96. D8×C67 | M16 | semidirect |
| 163. #1333 | D67 | semidirect |
| 164. C67 | #11666 | semidirect |
| 234. D8 | #11761611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14524062 | 2 |
| #22562010 | 2 |
| #22558963 | 2 |
| #22558180 | 2 |
| #22558178 | 2 |
| #22558176 | 2 |
| C67×#1333 | 2 |
| #11666 | 67 |