Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
572 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 97 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×#14556069 | C2 | semidirect |
| 2. C2×#17986266 | C2 | semidirect |
| 3. #22597989 | C2 | semidirect |
| 4. C2×#17985813 | C2 | semidirect |
| 5. C2×#17985784 | C2 | semidirect |
| 6. #22586435 | C2 | semidirect |
| 7. C71×#2140 | C2 | semidirect |
| 56. C2×C71⋊C16 | D4 | semidirect |
| 58. #14556064 | D4 | semidirect |
| 67. C2×D8×C71 | D4 | semidirect |
| 204. #2140 | D71 | semidirect |
| 207. C71 | #13319 | semidirect |
| 247. C2×D8 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556069 | 2 |
| C2×#17986266 | 2 |
| #22597989 | 2 |
| C2×#17985813 | 2 |
| C2×#17985784 | 2 |
| #22586435 | 2 |
| C71×#2140 | 2 |
| #13319 | 71 |