Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
854 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 203 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 |
|---|---|---|
| 1. C22×#14556071 | C2 | semidirect |
| 3. C2×#17986384 | C2 | semidirect |
| 4. #22590602 | C2 | direct (N × H) |
| 5. C2×C16×Dic71 | C2 | semidirect |
| 6. C22×Q32×C71 | C2 | semidirect |
| 11. C2×#14556071 | C22 | semidirect |
| 16. #17986384 | C22 | semidirect |
| 18. C16×Dic71 | C22 | semidirect |
| 21. C2×Q32×C71 | C22 | semidirect |
| 114. C2×C71 | #2249 | semidirect |
| 118. C22×Q32 | D71 | semidirect |
| 124. C71 | C2×#2249 | semidirect |
| 130. C2×Q32 | C2×D71 | semidirect |
| 232. C2 | #22590602 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556071 | 2 |
| C22×D1136 | 2 |
| C2×#17986384 | 2 |
| #22590602 | 2 |
| C2×C16×Dic71 | 2 |
| C22×Q32×C71 | 2 |
| C2×#2249 | 71 |