Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
3262 conjugacy classes of subgroups; only the 1067 normal subgroups are shown.
This group has 3262 conjugacy classes of subgroups — too many to draw. Only its 1067 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. C2×#17986379 | C2 | direct (N × H) |
| 11. #17986379 | C22 | direct (N × H) |
| 40. C22×C4×C71 | Q16 | semidirect |
| 53. C2×C4×C71 | C2×Q16 | semidirect |
| 63. C22×C71 | #494 | semidirect |
| 68. C4×C71 | C22×Q16 | semidirect |
| 72. C2×C71 | C2×#494 | semidirect |
| 79. C71 | C22×#494 | semidirect |
| 113. C22×C4 | Dic284 | semidirect |
| 132. C2×C4 | C2×Dic284 | semidirect |
| 138. C22 | #17986379 | direct (N × H) |
| 144. C4 | C22×Dic284 | semidirect |
| 146. C2 | C2×#17986379 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic284 | 2 |
| C22×#14556128 | 2 |
| C2×#17986379 | 2 |
| C22×C4×C8×C71 | 2 |
| C22×#494 | 71 |