Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
| 3. Q16×C71⋊C8 | C2 | semidirect |
| 4. #22586403 | C2 | semidirect |
| 5. #22586397 | C2 | semidirect |
| 59. Q16×C71 | SD16 | semidirect |
| 116. C71 | #12419 | semidirect |
| 160. Q16 | #11765853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590492 | 2 |
| #22587929 | 2 |
| Q16×C71⋊C8 | 2 |
| #22586403 | 2 |
| #22586397 | 2 |
| #22586386 | 2 |
| C71×#2207 | 2 |
| #12419 | 71 |