Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
994 conjugacy classes of subgroups; only the 475 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 475 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. #22586642 | C2 | direct (N × H) |
| 3. C2×#17985720 | C2 | semidirect |
| 4. C2×C82×C71 | C2 | semidirect |
| 11. #17985720 | C22 | semidirect |
| 13. C82×C71 | C22 | semidirect |
| 39. C2×C8×C71 | M16 | semidirect |
| 53. C8×C71 | C2×M16 | semidirect |
| 63. C2×C71 | #1455 | semidirect |
| 69. C2×C82 | D71 | semidirect |
| 70. C71 | C2×#1455 | semidirect |
| 79. C82 | C2×D71 | semidirect |
| 103. C2×C8 | #11765848 | semidirect |
| 120. C8 | C2×#11765848 | semidirect |
| 129. C2 | #22586642 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11765848 | 2 |
| #22586642 | 2 |
| C2×#17985720 | 2 |
| C2×C82×C71 | 2 |
| C2×#1455 | 71 |