Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22569925 | C2 | semidirect |
| 2. #22569853 | C2 | semidirect |
| 3. C2×#16863209 | C2 | semidirect |
| 4. #22561945 | C2 | semidirect |
| 5. #22561838 | C2 | semidirect |
| 6. #22558324 | C2 | semidirect |
| 7. C2×#509×C67 | C2 | semidirect |
| 54. #14523979 | D4 | semidirect |
| 66. C2×Q16×C67 | D4 | semidirect |
| 74. C2×D8×C67 | D4 | semidirect |
| 79. M32×C67 | D4 | semidirect |
| 212. C2×#509 | D67 | semidirect |
| 219. C67 | #13310 | semidirect |
| 255. C2×Q16 | C22⋊D67 | semidirect |
| 263. C2×D8 | C22⋊D67 | semidirect |
| 283. M32 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569925 | 2 |
| #22569853 | 2 |
| C2×#16863209 | 2 |
| #22561945 | 2 |
| #22561838 | 2 |
| #22558324 | 2 |
| C2×#509×C67 | 2 |
| #13310 | 67 |