Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
460 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 29. #14556074 | Q8 | direct (N × H) |
| 72. Q8×C71 | Q32 | semidirect |
| 106. C71 | Q8×Q32 | semidirect |
| 174. Q8 | #14556074 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic284 | 2 |
| #22590613 | 2 |
| #22590492 | 2 |
| #22590489 | 2 |
| Q8×C71⋊C16 | 2 |
| C4×#14556074 | 2 |
| Q8×Q16×C71 | 2 |
| Q8×Q32 | 71 |