Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
614 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22569681 | C2 | semidirect |
| 3. C2×#16863596 | C2 | semidirect |
| 4. #22558876 | C2 | semidirect |
| 5. #22558609 | C2 | semidirect |
| 6. #22558105 | C2 | semidirect |
| 7. C67×#1461 | C2 | semidirect |
| 121. C2×Q8×C67 | D8 | semidirect |
| 227. #1461 | D67 | semidirect |
| 229. C67 | #10177 | semidirect |
| 312. C2×Q8 | D536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571129 | 2 |
| #22569681 | 2 |
| C2×#16863596 | 2 |
| #22558876 | 2 |
| #22558609 | 2 |
| #22558105 | 2 |
| C67×#1461 | 2 |
| #10177 | 67 |