Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
594 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #22589321 | C2 | semidirect |
| 5. #22586905 | C2 | semidirect |
| 6. #22586199 | C2 | semidirect |
| 7. C71×#1274 | C2 | semidirect |
| 11. #17986372 | C4 | semidirect |
| 12. #17986346 | C4 | semidirect |
| 33. #14556128 | C2×C4 | semidirect |
| 34. #14556128 | C2×C4 | semidirect |
| 64. C4×C8×C71 | C2×C4 | semidirect |
| 113. C42×C71 | SD16 | semidirect |
| 201. #1274 | D71 | semidirect |
| 202. C71 | #9295 | semidirect |
| 257. C4×C8 | C4×D71 | semidirect |
| 308. C42 | #11765854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599283 | 2 |
| #22591065 | 2 |
| #22589321 | 2 |
| #22587007 | 2 |
| #22586905 | 2 |
| #22586199 | 2 |
| C71×#1274 | 2 |
| #9295 | 71 |