Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
224 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22590245 | C2 | semidirect |
| 4. #22586318 | C2 | semidirect |
| 6. C8×C71⋊C16 | C2 | semidirect |
| 7. C71×#1367 | C2 | semidirect |
| 59. C71⋊C16 | SD16 | semidirect |
| 84. C8×C71 | M32 | semidirect |
| 109. #1367 | D71 | semidirect |
| 113. C71 | #12051 | semidirect |
| 192. C8 | #14556067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590245 | 2 |
| #22590171 | 2 |
| C8×#11765854 | 2 |
| #22586318 | 2 |
| #22586294 | 2 |
| C8×C71⋊C16 | 2 |
| C71×#1367 | 2 |
| #12051 | 71 |