Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
466 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 135 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. #22561836 | C2 | semidirect |
| 3. #22561830 | C2 | semidirect |
| 4. #22558288 | C2 | semidirect |
| 5. C67×#3407 | C2 | semidirect |
| 54. C2×C16×C67 | D4 | semidirect |
| 143. #3407 | D67 | semidirect |
| 148. C67 | #12988 | semidirect |
| 192. C2×C16 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568925 | 2 |
| #22561836 | 2 |
| #22561830 | 2 |
| #22558288 | 2 |
| C67×#3407 | 2 |
| #12988 | 67 |