Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
7646 conjugacy classes of subgroups; only the 1976 normal subgroups are shown.
This group has 7646 conjugacy classes of subgroups — too many to draw. Only its 1976 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. C24×#10596833 | C2 | semidirect |
| 2. C22×#14556648 | C2 | direct (N × H) |
| 5. C23×#10596833 | C22 | semidirect |
| 6. C2×#14556648 | C22 | direct (N × H) |
| 14. C22×#10596833 | C23 | semidirect |
| 15. #14556648 | C23 | direct (N × H) |
| 18. C24×D73 | C8 | semidirect |
| 31. C2×#10596833 | C24 | semidirect |
| 35. C23×D73 | C2×C8 | semidirect |
| 51. C23×C73 | C22⋊C8 | semidirect |
| 59. C22×D73 | C22×C8 | semidirect |
| 70. C22×C73 | C2×C22⋊C8 | semidirect |
| 78. C2×D73 | C23×C8 | semidirect |
| 83. C2×C73 | C22×C22⋊C8 | semidirect |
| 91. C73 | C23×C22⋊C8 | semidirect |
| 144. C23 | #14556648 | direct (N × H) |
| 162. C22 | C2×#14556648 | direct (N × H) |
| 171. C2 | C22×#14556648 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#10596833 | 2 |
| C22×#14556648 | 2 |
| C24×C4×D73 | 2 |
| C23×C22⋊C8 | 73 |