Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
508 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22561136 | C2 | semidirect |
| 3. #22561049 | C2 | semidirect |
| 4. #22558961 | C2 | semidirect |
| 5. #22558886 | C2 | semidirect |
| 6. #22558112 | C2 | semidirect |
| 7. C67×#1980 | C2 | semidirect |
| 111. M16×C67 | D8 | semidirect |
| 210. #1980 | D67 | semidirect |
| 215. C67 | #10500 | semidirect |
| 314. M16 | #11761613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571124 | 2 |
| #22561136 | 2 |
| #22561049 | 2 |
| #22558961 | 2 |
| #22558886 | 2 |
| #22558112 | 2 |
| C67×#1980 | 2 |
| #10500 | 67 |