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 |
| 4. C4×#14556060 | C2 | semidirect |
| 5. #22588171 | C2 | semidirect |
| 7. C71×#1726 | C2 | semidirect |
| 11. C4×#11765854 | C4 | semidirect |
| 30. C4×Dic142 | C2×C4 | semidirect |
| 40. #14556060 | C2×C4 | semidirect |
| 41. #14556053 | C2×C4 | semidirect |
| 49. C4×C8×C71 | C2×C4 | semidirect |
| 62. #11765854 | C42 | semidirect |
| 128. #1726 | D71 | semidirect |
| 129. C71 | #20506 | semidirect |
| 169. C4×C8 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11765854 | 2 |
| #22590703 | 2 |
| #22590702 | 2 |
| C4×#14556060 | 2 |
| #22588171 | 2 |
| #22588166 | 2 |
| C71×#1726 | 2 |
| #20506 | 71 |