Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
506 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 165 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. #22601346 | C2 | semidirect |
| 3. #22590568 | C2 | semidirect |
| 4. #22590483 | C2 | semidirect |
| 7. Q8×C16×C71 | C2 | semidirect |
| 72. Q8×C71 | SD32 | semidirect |
| 109. Q8×C16 | D71 | semidirect |
| 111. C71 | #33926 | semidirect |
| 179. Q8 | #14556073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601346 | 2 |
| Q8×D568 | 2 |
| #22590568 | 2 |
| #22590483 | 2 |
| #22590386 | 2 |
| C4×#14556073 | 2 |
| Q8×C16×C71 | 2 |
| #33926 | 71 |