Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
294 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #22586392 | C2 | semidirect |
| 5. #22586322 | C2 | semidirect |
| 6. #22586310 | C2 | semidirect |
| 7. C71×#3390 | C2 | semidirect |
| 75. Q16×C71 | SD16 | semidirect |
| 140. #3390 | D71 | semidirect |
| 147. C71 | #12361 | semidirect |
| 208. Q16 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590583 | 2 |
| #22590380 | 2 |
| #22587824 | 2 |
| #22586392 | 2 |
| #22586322 | 2 |
| #22586310 | 2 |
| C71×#3390 | 2 |
| #12361 | 71 |