Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 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. #26042307 | C2 | semidirect |
| 2. D4×#13089685 | C2 | semidirect |
| 3. #26042141 | C2 | semidirect |
| 4. #26042127 | C2 | semidirect |
| 5. D4⋊#13089685 | C2 | semidirect |
| 6. #26042120 | C2 | semidirect |
| 33. #15668434 | C8 | semidirect |
| 49. D724 | C2×C8 | semidirect |
| 57. #13089678 | C2×C8 | semidirect |
| 60. D4×C181 | C2×C8 | semidirect |
| 83. C181 | #1580 | semidirect |
| 131. D4 | D181⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042307 | 2 |
| D4×#13089685 | 2 |
| #26042141 | 2 |
| #26042127 | 2 |
| D4⋊#13089685 | 2 |
| #26042120 | 2 |
| #26041359 | 2 |
| #1580 | 181 |