Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22590106 | C2 | semidirect |
| 2. #22589968 | C2 | semidirect |
| 3. C2×#17985781 | C2 | semidirect |
| 4. #22589945 | C2 | semidirect |
| 24. #14556068 | D4 | semidirect |
| 144. C71 | #13201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590106 | 2 |
| #22589968 | 2 |
| C2×#17985781 | 2 |
| #22589945 | 2 |
| C71×#2930 | 2 |
| #13201 | 71 |