Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#19153839 | C2 | semidirect |
| 2. C2×Q16×D181 | C2 | semidirect |
| 3. #26041941 | C2 | semidirect |
| 4. #26041663 | C2 | semidirect |
| 5. #26041521 | C2 | semidirect |
| 6. #26041516 | C2 | semidirect |
| 7. #26041501 | C2 | semidirect |
| 8. #26041444 | C2 | semidirect |
| 9. #26041419 | C2 | semidirect |
| 10. C8×D724 | C2 | semidirect |
| 11. C4×Q16×C181 | C2 | semidirect |
| 73. Q16×C181 | D4 | semidirect |
| 120. C2×D181 | #135 | semidirect |
| 136. C181 | #3285 | semidirect |
| 147. C4×Q16 | D181 | semidirect |
| 195. Q16 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153839 | 2 |
| C2×Q16×D181 | 2 |
| #26041941 | 2 |
| #26041663 | 2 |
| #26041521 | 2 |
| #26041516 | 2 |
| #26041501 | 2 |
| #26041444 | 2 |
| #26041419 | 2 |
| C8×D724 | 2 |
| C4×Q16×C181 | 2 |
| #3285 | 181 |