Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
906 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 211 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. #22598915 | C2 | semidirect |
| 2. #22598768 | C2 | semidirect |
| 3. #22588012 | C2 | semidirect |
| 4. #22588009 | C2 | semidirect |
| 5. #22588007 | C2 | semidirect |
| 6. #22588004 | C2 | semidirect |
| 7. C2×#17985720 | C2 | semidirect |
| 8. C71×#3147 | C2 | semidirect |
| 88. C2×C8×C71 | D8 | semidirect |
| 141. #3147 | D71 | semidirect |
| 147. C71 | #19616 | semidirect |
| 225. C2×C8 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598915 | 2 |
| #22598768 | 2 |
| #22588012 | 2 |
| #22588009 | 2 |
| #22588007 | 2 |
| #22588004 | 2 |
| C2×#17985720 | 2 |
| C71×#3147 | 2 |
| #19616 | 71 |