Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 246 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 |
|---|---|---|
| 1. #22590596 | C2 | semidirect |
| 2. #22587705 | C2 | semidirect |
| 4. #22586412 | C2 | semidirect |
| 5. #22586390 | C2 | semidirect |
| 6. #22586387 | C2 | semidirect |
| 7. C71×#2169 | C2 | semidirect |
| 73. C16×C71 | D8 | semidirect |
| 119. #2169 | D71 | semidirect |
| 125. C71 | #12435 | semidirect |
| 191. C16 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590596 | 2 |
| #22587705 | 2 |
| #22587695 | 2 |
| #22586412 | 2 |
| #22586390 | 2 |
| #22586387 | 2 |
| C71×#2169 | 2 |
| #12435 | 71 |