Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
604 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 604 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 |
|---|---|---|
| 1. C2×#16863834 | C2 | semidirect |
| 2. #22569819 | C2 | semidirect |
| 3. C2×#16863650 | C2 | semidirect |
| 4. C2×#16863205 | C2 | semidirect |
| 5. #22561924 | C2 | semidirect |
| 6. C2×#16863177 | C2 | semidirect |
| 7. C67×#1386 | C2 | semidirect |
| 39. C2×Dic268 | D4 | semidirect |
| 46. C2×D536 | D4 | semidirect |
| 47. C2×D536 | D4 | semidirect |
| 75. M32×C67 | D4 | semidirect |
| 77. #107×C67 | D4 | semidirect |
| 80. #106×C67 | D4 | semidirect |
| 227. #1386 | D67 | semidirect |
| 228. C67 | #13316 | semidirect |
| 292. M32 | D268 | semidirect |
| 295. #107 | D268 | semidirect |
| 298. #106 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863834 | 2 |
| #22569819 | 2 |
| C2×#16863650 | 2 |
| C2×#16863205 | 2 |
| #22561924 | 2 |
| C2×#16863177 | 2 |
| C67×#1386 | 2 |
| #13316 | 67 |