Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2846 conjugacy classes of subgroups; only the 1208 normal subgroups are shown.
This group has 2846 conjugacy classes of subgroups — too many to draw. Only its 1208 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. C22×#14556662 | C2 | direct (N × H) |
| 7. C2×#14556662 | C22 | direct (N × H) |
| 16. #14556662 | C23 | direct (N × H) |
| 48. C23×C73 | #108 | semidirect |
| 66. C22×C73 | C2×#108 | semidirect |
| 77. C2×C73 | C22×#108 | semidirect |
| 84. C73 | C23×#108 | semidirect |
| 133. C23 | #14556662 | direct (N × H) |
| 151. C22 | C2×#14556662 | direct (N × H) |
| 159. C2 | C22×#14556662 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11924038 | 2 |
| C22×#14556662 | 2 |
| C23×C8×D73 | 2 |
| C23×#108 | 73 |