Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
442 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 442 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 |
|---|---|---|
| 3. #22586370 | C2 | semidirect |
| 4. #22586274 | C2 | semidirect |
| 5. C71×#2811 | C2 | semidirect |
| 72. C2×Q8×C71 | SD16 | semidirect |
| 145. #2811 | D71 | semidirect |
| 150. C71 | #12130 | semidirect |
| 204. C2×Q8 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22589386 | 2 |
| #22587308 | 2 |
| #22586370 | 2 |
| #22586274 | 2 |
| C71×#2811 | 2 |
| #12130 | 71 |