Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
758 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 1. #22571127 | C2 | semidirect |
| 2. #22570661 | C2 | semidirect |
| 3. C2×#16863772 | C2 | semidirect |
| 4. #22558878 | C2 | semidirect |
| 5. #22558659 | C2 | semidirect |
| 6. #22558047 | C2 | semidirect |
| 7. C67×#1965 | C2 | semidirect |
| 119. M16×C67 | D8 | semidirect |
| 206. #1965 | D67 | semidirect |
| 210. C67 | #10144 | semidirect |
| 315. M16 | #11761613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571127 | 2 |
| #22570661 | 2 |
| C2×#16863772 | 2 |
| #22558878 | 2 |
| #22558659 | 2 |
| #22558047 | 2 |
| C67×#1965 | 2 |
| #10144 | 67 |