Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
150 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 27. C71⋊C32 | Q8 | semidirect |
| 31. C32×C71 | Q8 | semidirect |
| 77. C71 | #13734 | semidirect |
| 101. C32 | Dic142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590617 | 2 |
| #22590614 | 2 |
| #22586542 | 2 |
| #22586541 | 2 |
| #22586539 | 2 |
| #22586473 | 2 |
| C71×#1423 | 2 |
| #13734 | 71 |