Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
878 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 239 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 |
|---|---|---|
| 3. #22559827 | C2 | semidirect |
| 4. #22559826 | C2 | semidirect |
| 5. #22559825 | C2 | semidirect |
| 7. C67×#1713 | C2 | semidirect |
| 57. C8×D67 | Q16 | semidirect |
| 82. C8×C67 | C2×Q16 | semidirect |
| 84. C67⋊C8 | C2×Q16 | semidirect |
| 97. D67 | #1713 | direct (N × H) |
| 103. #1713 | D67 | direct (N × H) |
| 105. C67 | C2×#1713 | semidirect |
| 182. C8 | Q16×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D67 | 2 |
| #494×D67 | 2 |
| #22559827 | 2 |
| #22559826 | 2 |
| #22559825 | 2 |
| C82×D67 | 2 |
| C67×#1713 | 2 |
| C2×#1713 | 67 |