Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
238 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22559093 | C2 | semidirect |
| 3. #22558169 | C2 | semidirect |
| 4. C16×C67⋊C8 | C2 | semidirect |
| 5. C67×#1371 | C2 | semidirect |
| 46. C16×C67 | M16 | semidirect |
| 62. C67⋊C8 | D16 | semidirect |
| 80. #1371 | D67 | semidirect |
| 83. C67 | #12081 | semidirect |
| 124. C16 | #11761611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1072 | 2 |
| #22559093 | 2 |
| #22558169 | 2 |
| C16×C67⋊C8 | 2 |
| C67×#1371 | 2 |
| #12081 | 67 |