Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
906 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 227 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. #22598919 | C2 | semidirect |
| 2. #22598768 | C2 | semidirect |
| 3. #22588011 | C2 | semidirect |
| 4. #22588006 | C2 | semidirect |
| 5. C2×#322×C71 | C2 | semidirect |
| 55. C2×C8×C71 | D8 | semidirect |
| 96. C2×#322 | D71 | semidirect |
| 97. C71 | #19616 | semidirect |
| 145. C2×C8 | D568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598919 | 2 |
| #22598768 | 2 |
| #22588011 | 2 |
| #22588006 | 2 |
| C2×#322×C71 | 2 |
| #19616 | 71 |