Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
496 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22596976 | C2 | semidirect |
| 3. #22586939 | C2 | semidirect |
| 4. #22586937 | C2 | semidirect |
| 5. #22586672 | C2 | semidirect |
| 6. #22586233 | C2 | semidirect |
| 7. C71×#1300 | C2 | semidirect |
| 61. #14556039 | D4 | semidirect |
| 71. #97×C71 | D4 | semidirect |
| 225. #1300 | D71 | semidirect |
| 226. C71 | #9389 | semidirect |
| 287. #97 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596976 | 2 |
| #22594021 | 2 |
| #22586939 | 2 |
| #22586937 | 2 |
| #22586672 | 2 |
| #22586233 | 2 |
| C71×#1300 | 2 |
| #9389 | 71 |