Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
298 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. #22562436 | C2 | semidirect |
| 3. #22562256 | C2 | semidirect |
| 4. #22558268 | C2 | semidirect |
| 5. #22558172 | C2 | semidirect |
| 89. D4×C67 | Q32 | semidirect |
| 135. C67 | #12346 | semidirect |
| 220. D4 | #14523989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22572602 | 2 |
| #22562436 | 2 |
| #22562256 | 2 |
| #22558268 | 2 |
| #22558172 | 2 |
| D4⋊(C67⋊C16) | 2 |
| C67×#1669 | 2 |
| #12346 | 67 |