Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#16863831 | C2 | semidirect |
| 2. #22569925 | C2 | semidirect |
| 3. #22569858 | C2 | semidirect |
| 4. C2×#16863210 | C2 | semidirect |
| 5. #22561836 | C2 | semidirect |
| 6. #22558325 | C2 | semidirect |
| 7. C67×#2145 | C2 | semidirect |
| 59. #14523983 | D4 | semidirect |
| 62. #14523979 | D4 | semidirect |
| 71. C2×Q16×C67 | D4 | semidirect |
| 73. C2×D8×C67 | D4 | semidirect |
| 216. #2145 | D67 | semidirect |
| 219. C67 | #13310 | semidirect |
| 255. C2×Q16 | D268 | semidirect |
| 263. C2×D8 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863831 | 2 |
| #22569925 | 2 |
| #22569858 | 2 |
| C2×#16863210 | 2 |
| #22561836 | 2 |
| #22558325 | 2 |
| C67×#2145 | 2 |
| #13310 | 67 |