Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
648 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 648 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. C2×#17986394 | C2 | semidirect |
| 2. C2×#17986358 | C2 | semidirect |
| 3. #22589312 | C2 | semidirect |
| 4. C2×#17985739 | C2 | semidirect |
| 5. C2×#17985739 | C2 | semidirect |
| 6. #22586221 | C2 | semidirect |
| 42. #14556128 | D4 | semidirect |
| 51. #14556039 | D4 | semidirect |
| 52. #14556039 | D4 | semidirect |
| 218. C71 | #10081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986394 | 2 |
| C2×#17986358 | 2 |
| #22589312 | 2 |
| C2×#17985739 | 2 |
| #22586221 | 2 |
| C71×#2819 | 2 |
| #10081 | 71 |