Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
262 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22590590 | C2 | semidirect |
| 2. #22590173 | C2 | semidirect |
| 3. #22587696 | C2 | semidirect |
| 4. #22586385 | C2 | semidirect |
| 5. C71×#1372 | C2 | semidirect |
| 54. C16×C71 | D8 | semidirect |
| 95. #1372 | D71 | semidirect |
| 97. C71 | #12433 | semidirect |
| 146. C16 | D568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590590 | 2 |
| #22590173 | 2 |
| #22587696 | 2 |
| #22586385 | 2 |
| C71×#1372 | 2 |
| #12433 | 71 |