Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
454 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 454 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 |
|---|---|---|
| 2. #22590025 | C2 | semidirect |
| 3. #22586496 | C2 | semidirect |
| 4. C71×#2126 | C2 | semidirect |
| 7. C2×#14556125 | C4 | semidirect |
| 8. #17986389 | C4 | semidirect |
| 13. C4×#11765849 | C4 | semidirect |
| 15. #17985796 | C22 | semidirect |
| 18. #354×C71 | C22 | semidirect |
| 159. #2126 | D71 | semidirect |
| 161. C71 | #13579 | semidirect |
| 175. #354 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598793 | 2 |
| #22590025 | 2 |
| #22586496 | 2 |
| C71×#2126 | 2 |
| #13579 | 71 |