Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. #26041534 | C2 | direct (N × H) |
| 4. C2×#19153748 | C2 | semidirect |
| 5. C2×#19153740 | C2 | semidirect |
| 6. C22×Q16×C181 | C2 | semidirect |
| 16. #19153748 | C22 | semidirect |
| 17. #19153740 | C22 | semidirect |
| 20. C2×Q16×C181 | C22 | semidirect |
| 79. C2×C181 | #470 | semidirect |
| 83. C181 | C2×#470 | semidirect |
| 85. C22×Q16 | D181 | semidirect |
| 94. C2×Q16 | C2×D181 | semidirect |
| 164. C2 | #26041534 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668432 | 2 |
| C2×#19153792 | 2 |
| #26041534 | 2 |
| C2×#19153748 | 2 |
| C2×#19153740 | 2 |
| C22×Q16×C181 | 2 |
| C2×#470 | 181 |