Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
372 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22562006 | C2 | semidirect |
| 3. #22558966 | C2 | semidirect |
| 4. #22558173 | C2 | semidirect |
| 5. #22558171 | C2 | semidirect |
| 6. #22558169 | C2 | semidirect |
| 7. C67×#1332 | C2 | semidirect |
| 74. D536 | M16 | semidirect |
| 95. Q16×C67 | M16 | semidirect |
| 164. #1332 | D67 | semidirect |
| 167. C67 | #11660 | semidirect |
| 234. Q16 | #11761611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14524066 | 2 |
| #22562006 | 2 |
| #22558966 | 2 |
| #22558173 | 2 |
| #22558171 | 2 |
| #22558169 | 2 |
| C67×#1332 | 2 |
| #11660 | 67 |