Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
174 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 57 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×D2896 | C2 | semidirect |
| 2. #26041515 | C2 | semidirect |
| 3. #26041105 | C2 | semidirect |
| 4. #26041081 | C2 | semidirect |
| 5. C22×C16×C181 | C2 | semidirect |
| 27. C16×C181 | D4 | semidirect |
| 43. C22×C181 | D16 | semidirect |
| 57. C181 | #2215 | semidirect |
| 60. C22×C16 | D181 | semidirect |
| 85. C16 | C22⋊D181 | semidirect |
| 104. C22 | D2896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D2896 | 2 |
| #26041515 | 2 |
| #26041105 | 2 |
| #26041081 | 2 |
| C22×C16×C181 | 2 |
| #2215 | 181 |