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. Q16×C67⋊C8 | C2 | semidirect |
| 4. #22558280 | C2 | semidirect |
| 6. #22558128 | C2 | semidirect |
| 7. C67×#1332 | C2 | semidirect |
| 59. Q16×C67 | M16 | semidirect |
| 110. #1332 | D67 | semidirect |
| 113. C67 | #12075 | semidirect |
| 154. Q16 | #11761611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523986 | 2 |
| #22559093 | 2 |
| Q16×C67⋊C8 | 2 |
| #22558280 | 2 |
| #22558171 | 2 |
| #22558128 | 2 |
| C67×#1332 | 2 |
| #12075 | 67 |