Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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. C16×Dic134 | C2 | semidirect |
| 4. #22558273 | C2 | semidirect |
| 5. #22558189 | C2 | semidirect |
| 7. C67×#1311 | C2 | semidirect |
| 67. C16×C67 | SD16 | semidirect |
| 80. Dic134 | M32 | semidirect |
| 112. #1311 | D67 | semidirect |
| 113. C67 | #12050 | semidirect |
| 173. C16 | #11761617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic134 | 2 |
| #22562042 | 2 |
| C8×#11761617 | 2 |
| #22558273 | 2 |
| #22558189 | 2 |
| #22558165 | 2 |
| C67×#1311 | 2 |
| #12050 | 67 |