Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
332 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×C4×C67⋊C16 | C2 | semidirect |
| 5. #22558304 | C2 | semidirect |
| 6. #22558302 | C2 | semidirect |
| 7. C67×#1945 | C2 | semidirect |
| 15. #16863199 | C4 | semidirect |
| 16. #16863196 | C4 | semidirect |
| 142. #1945 | D67 | semidirect |
| 145. C67 | #13151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863202 | 2 |
| #22561914 | 2 |
| C2×C4×C67⋊C16 | 2 |
| #22561097 | 2 |
| #22558304 | 2 |
| #22558302 | 2 |
| C67×#1945 | 2 |
| #13151 | 67 |