Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1072 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 175 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. #22598889 | C2 | semidirect |
| 3. #22598158 | C2 | semidirect |
| 4. #22589550 | C2 | semidirect |
| 5. #22589321 | C2 | semidirect |
| 6. #22589181 | C2 | semidirect |
| 7. #22588549 | C2 | semidirect |
| 8. #22588151 | C2 | semidirect |
| 9. C71×#2641 | C2 | semidirect |
| 102. #11765849 | #41 | semidirect |
| 203. #2641 | D71 | semidirect |
| 209. C71 | #25690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602214 | 2 |
| #22598889 | 2 |
| #22598158 | 2 |
| #22589550 | 2 |
| #22589321 | 2 |
| #22589181 | 2 |
| #22588549 | 2 |
| #22588151 | 2 |
| C71×#2641 | 2 |
| #25690 | 71 |