Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
906 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22598920 | C2 | semidirect |
| 2. #22598918 | C2 | semidirect |
| 3. #22598769 | C2 | semidirect |
| 4. #22598763 | C2 | semidirect |
| 5. #22588012 | C2 | semidirect |
| 6. #22588010 | C2 | semidirect |
| 7. #22588008 | C2 | semidirect |
| 8. #22588006 | C2 | semidirect |
| 9. #22588004 | C2 | semidirect |
| 10. #322×D71 | C2 | semidirect |
| 11. C71×#1722 | C2 | semidirect |
| 116. C8×D71 | D8 | semidirect |
| 199. #1722 | D71 | semidirect |
| 204. C71 | #19616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598920 | 2 |
| #22598918 | 2 |
| #22598769 | 2 |
| #22598763 | 2 |
| #22588012 | 2 |
| #22588010 | 2 |
| #22588008 | 2 |
| #22588006 | 2 |
| #22588004 | 2 |
| #322×D71 | 2 |
| C71×#1722 | 2 |
| #19616 | 71 |