Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
614 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 614 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 |
|---|---|---|
| 2. C2×#16863596 | C2 | semidirect |
| 3. #22558878 | C2 | semidirect |
| 4. #22558608 | C2 | semidirect |
| 5. #22558533 | C2 | semidirect |
| 6. #22558104 | C2 | semidirect |
| 7. C67×#3037 | C2 | semidirect |
| 109. C2×Q8×C67 | D8 | semidirect |
| 223. #3037 | D67 | semidirect |
| 229. C67 | #10177 | semidirect |
| 312. C2×Q8 | #11761613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571124 | 2 |
| C2×#16863596 | 2 |
| #22558878 | 2 |
| #22558608 | 2 |
| #22558533 | 2 |
| #22558104 | 2 |
| C67×#3037 | 2 |
| #10177 | 67 |