Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
658 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. #22593339 | C2 | semidirect |
| 3. #22587009 | C2 | semidirect |
| 4. #22586835 | C2 | semidirect |
| 5. #22586735 | C2 | semidirect |
| 6. #22586241 | C2 | semidirect |
| 7. C71×#3037 | C2 | semidirect |
| 111. C2×Q8×C71 | D8 | semidirect |
| 228. #3037 | D71 | semidirect |
| 234. C71 | #10242 | semidirect |
| 317. C2×Q8 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599255 | 2 |
| #22593339 | 2 |
| #22587009 | 2 |
| #22586835 | 2 |
| #22586735 | 2 |
| #22586241 | 2 |
| C71×#3037 | 2 |
| #10242 | 71 |