Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
992 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 309 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. C22×#15668433 | C2 | semidirect |
| 2. C2×#19153733 | C2 | direct (N × H) |
| 5. C2×#15668433 | C22 | semidirect |
| 7. #19153733 | C22 | direct (N × H) |
| 15. #15668433 | C23 | semidirect |
| 57. C22×C181 | #100 | semidirect |
| 66. C2×C181 | C2×#100 | semidirect |
| 68. C181 | C22×#100 | semidirect |
| 126. C22 | #19153733 | direct (N × H) |
| 135. C2 | C2×#19153733 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668433 | 2 |
| C2×#19153733 | 2 |
| C23×D4×C181 | 2 |
| C22×#100 | 181 |