Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
274 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22590381 | C2 | semidirect |
| 3. C8×Dic284 | C2 | semidirect |
| 4. #22586387 | C2 | semidirect |
| 5. C71×#1370 | C2 | semidirect |
| 40. Dic284 | D8 | semidirect |
| 74. C8×C71 | SD32 | semidirect |
| 97. #1370 | D71 | semidirect |
| 99. C71 | #12425 | semidirect |
| 169. C8 | #14556073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590381 | 2 |
| #22587955 | 2 |
| C8×Dic284 | 2 |
| #22586387 | 2 |
| C71×#1370 | 2 |
| #12425 | 71 |