Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1342 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1342 conjugacy classes of subgroups — too many to draw. Only its 283 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×#16863773 | C2 | semidirect |
| 2. C2×#16863772 | C2 | semidirect |
| 3. #22559823 | C2 | direct (N × H) |
| 4. C2×C8×C67⋊C8 | C2 | semidirect |
| 5. C2×#493×C67 | C2 | semidirect |
| 10. #16863773 | C22 | semidirect |
| 12. #16863772 | C22 | semidirect |
| 14. C8×C67⋊C8 | C22 | semidirect |
| 18. #493×C67 | C22 | semidirect |
| 52. C2×C67⋊C8 | D8 | semidirect |
| 64. C2×C8×C67 | D8 | semidirect |
| 90. C8×C67 | C2×D8 | semidirect |
| 91. C67⋊C8 | C2×D8 | semidirect |
| 107. C2×C67 | #1712 | semidirect |
| 113. C2×#493 | D67 | semidirect |
| 116. C67 | C2×#1712 | semidirect |
| 127. #493 | C2×D67 | semidirect |
| 175. C2×C8 | #11761613 | semidirect |
| 202. C8 | C2×#11761613 | semidirect |
| 218. C2 | #22559823 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863773 | 2 |
| C2×#16863772 | 2 |
| #22559823 | 2 |
| C2×C8×C67⋊C8 | 2 |
| C2×#493×C67 | 2 |
| C2×#1712 | 67 |