Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
412 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22596018 | C2 | semidirect |
| 2. #22589566 | C2 | semidirect |
| 3. #22587377 | C2 | semidirect |
| 4. #22586368 | C2 | semidirect |
| 5. #22586343 | C2 | semidirect |
| 6. #22586283 | C2 | semidirect |
| 199. C71 | #12141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596018 | 2 |
| #22589566 | 2 |
| #22587377 | 2 |
| #22586368 | 2 |
| #22586343 | 2 |
| #22586283 | 2 |
| C71×#1598 | 2 |
| #12141 | 71 |