Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
540 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22570610 | C2 | semidirect |
| 3. #22566077 | C2 | semidirect |
| 4. #22558835 | C2 | semidirect |
| 5. #22558757 | C2 | semidirect |
| 6. #22558074 | C2 | semidirect |
| 7. C67×#1490 | C2 | semidirect |
| 208. #1490 | D67 | semidirect |
| 210. C67 | #10019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570610 | 2 |
| #22570300 | 2 |
| #22566077 | 2 |
| #22558835 | 2 |
| #22558757 | 2 |
| #22558074 | 2 |
| C67×#1490 | 2 |
| #10019 | 67 |