Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22597000 | C2 | semidirect |
| 3. #22588437 | C2 | semidirect |
| 6. #22586187 | C2 | semidirect |
| 7. C71×#1293 | C2 | semidirect |
| 17. C2×#14556062 | C4 | semidirect |
| 18. C2×#14556060 | C4 | semidirect |
| 20. C2×#14556050 | C4 | semidirect |
| 21. C2×#14556050 | C4 | semidirect |
| 229. #1293 | D71 | semidirect |
| 231. C71 | #9242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986324 | 2 |
| #22597000 | 2 |
| #22588437 | 2 |
| #22586857 | 2 |
| #22586701 | 2 |
| #22586187 | 2 |
| C71×#1293 | 2 |
| #9242 | 71 |