Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
368 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. #22590143 | C2 | semidirect |
| 3. #22586309 | C2 | semidirect |
| 4. #22586306 | C2 | semidirect |
| 5. C71×#1566 | C2 | semidirect |
| 65. Dic284 | M16 | semidirect |
| 68. D568 | M16 | semidirect |
| 150. #1566 | D71 | semidirect |
| 153. C71 | #11666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556150 | 2 |
| #22590143 | 2 |
| #22586309 | 2 |
| #22586306 | 2 |
| C71×#1566 | 2 |
| #11666 | 71 |