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 |
|---|---|---|
| 2. #22590567 | C2 | semidirect |
| 3. #22590482 | C2 | semidirect |
| 5. Q8×C71⋊C16 | C2 | semidirect |
| 7. C71×#3395 | C2 | semidirect |
| 74. Q8×C71 | SD32 | semidirect |
| 104. #3395 | D71 | semidirect |
| 111. C71 | #33926 | semidirect |
| 179. Q8 | #14556071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D568 | 2 |
| #22590567 | 2 |
| #22590482 | 2 |
| #22590382 | 2 |
| Q8×C71⋊C16 | 2 |
| C4×#14556071 | 2 |
| C71×#3395 | 2 |
| #33926 | 71 |