Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 1. #22590492 | C2 | semidirect |
| 4. #22586404 | C2 | semidirect |
| 5. #22586399 | C2 | semidirect |
| 7. C8×Q16×C71 | C2 | semidirect |
| 59. Q16×C71 | SD16 | semidirect |
| 112. C8×Q16 | D71 | semidirect |
| 116. C71 | #12419 | semidirect |
| 160. Q16 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590492 | 2 |
| #22590380 | 2 |
| #22587932 | 2 |
| #22586404 | 2 |
| #22586399 | 2 |
| #22586385 | 2 |
| C8×Q16×C71 | 2 |
| #12419 | 71 |