Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
496 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 496 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 |
|---|---|---|
| 74. Q8×C71 | Q32 | semidirect |
| 107. C71 | #33962 | semidirect |
| 176. Q8 | #14556074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601346 | 2 |
| #22590592 | 2 |
| #22590390 | 2 |
| #22590387 | 2 |
| Q8×C71⋊C16 | 2 |
| C4×#14556074 | 2 |
| C71×#3395 | 2 |
| #33962 | 71 |