Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
576 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. #22591452 | C2 | semidirect |
| 3. #22586849 | C2 | semidirect |
| 4. #22586232 | C2 | semidirect |
| 5. C71×#1533 | C2 | semidirect |
| 9. #17986394 | C4 | semidirect |
| 10. #17986389 | C4 | semidirect |
| 34. #14556128 | C2×C4 | semidirect |
| 35. #14556125 | C2×C4 | semidirect |
| 44. #14556039 | C2×C4 | semidirect |
| 173. #1533 | D71 | semidirect |
| 176. C71 | #9441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598804 | 2 |
| #22591452 | 2 |
| #22586849 | 2 |
| #22586232 | 2 |
| C71×#1533 | 2 |
| #9441 | 71 |