Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
890 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 110. C2×Q8×C67 | Q16 | semidirect |
| 183. C67 | #18221 | semidirect |
| 263. C2×Q8 | Dic268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574019 | 2 |
| #22570249 | 2 |
| #22565571 | 2 |
| #22559253 | 2 |
| #22559185 | 2 |
| #22558774 | 2 |
| C67×#1461 | 2 |
| #18221 | 67 |