Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
224 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22590248 | C2 | semidirect |
| 4. #22586404 | C2 | semidirect |
| 5. #22586320 | C2 | semidirect |
| 7. C8×C16×C71 | C2 | semidirect |
| 67. C16×C71 | SD16 | semidirect |
| 84. C8×C71 | M32 | semidirect |
| 112. C8×C16 | D71 | semidirect |
| 113. C71 | #12051 | semidirect |
| 173. C16 | #11765854 | semidirect |
| 192. C8 | #14556067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590248 | 2 |
| #22590173 | 2 |
| C8×#11765854 | 2 |
| #22586404 | 2 |
| #22586320 | 2 |
| #22586296 | 2 |
| C8×C16×C71 | 2 |
| #12051 | 71 |