Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1130 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 403 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. #22590703 | C2 | semidirect |
| 3. C4×#14556059 | C2 | semidirect |
| 4. #22588173 | C2 | semidirect |
| 6. #22588027 | C2 | semidirect |
| 10. C4×#11765853 | C4 | semidirect |
| 30. C4×Dic142 | C2×C4 | semidirect |
| 35. #14556059 | C2×C4 | semidirect |
| 36. #14556051 | C2×C4 | semidirect |
| 39. C4×C71⋊C8 | C2×C4 | semidirect |
| 56. #11765853 | C42 | semidirect |
| 129. C71 | #20506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11765853 | 2 |
| #22590703 | 2 |
| C4×#14556059 | 2 |
| #22588173 | 2 |
| #22588165 | 2 |
| #22588027 | 2 |
| C71×#2275 | 2 |
| #20506 | 71 |