Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
290 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22590375 | C2 | semidirect |
| 2. #22587955 | C2 | semidirect |
| 3. #22586410 | C2 | semidirect |
| 4. #22586385 | C2 | semidirect |
| 5. C8×D8×C71 | C2 | semidirect |
| 48. D8×C71 | D8 | semidirect |
| 78. C8×C71 | D16 | semidirect |
| 102. C8×D8 | D71 | semidirect |
| 105. C71 | #12424 | semidirect |
| 147. D8 | D568 | semidirect |
| 178. C8 | #14556069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590375 | 2 |
| #22587955 | 2 |
| #22586410 | 2 |
| #22586385 | 2 |
| C8×D8×C71 | 2 |
| #12424 | 71 |