Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 69. C8×C71 | Q32 | semidirect |
| 90. C71 | #12427 | semidirect |
| 154. C8 | #14556074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590390 | 2 |
| #22587958 | 2 |
| #22586410 | 2 |
| #22586388 | 2 |
| C8×Q16×C71 | 2 |
| #12427 | 71 |