Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22562007 | C2 | semidirect |
| 4. #22558168 | C2 | semidirect |
| 5. #22558167 | C2 | semidirect |
| 6. #22558166 | C2 | semidirect |
| 7. C67×#1330 | C2 | semidirect |
| 18. C4⋊(C67⋊C16) | C22 | semidirect |
| 22. #16863172 | C22 | semidirect |
| 25. C4⋊C16×C67 | C22 | semidirect |
| 26. #346×C67 | C22 | semidirect |
| 176. #1330 | D67 | semidirect |
| 177. C67 | #11634 | semidirect |
| 191. C4⋊C16 | C2×D67 | semidirect |
| 195. #346 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #436×D67 | 2 |
| #22562010 | 2 |
| #22562007 | 2 |
| #22558168 | 2 |
| #22558167 | 2 |
| #22558166 | 2 |
| C67×#1330 | 2 |
| #11634 | 67 |