Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
112 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 17 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C13×#89205 | C22 |
| Frattini | C3 | #64418⋊D13 |
| Fitting, socle | C3×C72×C13 | C2×D3 |
| LCS | G ▷ C13×#89205 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13⋊#11725071 | C2 | semidirect |
| 2. C13×#11725071 | C2 | semidirect |
| 3. #26039452 | C2 | semidirect |
| 5. C13×#89205 | C22 | semidirect |
| 13. C7⋊D91 | D9 | semidirect |
| 20. #11725071 | D13 | semidirect |
| 22. C72×C13 | C2×D9 | semidirect |
| 32. #89205 | C2×D13 | semidirect |
| 69. C72 | D9×D13 | semidirect |
| 97. C13 | #11725071⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13⋊#11725071 | 2 |
| C13×#11725071 | 2 |
| #26039452 | 2 |
| D21⋊D91 | 3 |
| #11725071⋊C2 | 13 |
| D9×D13 | 49 |