Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
852 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D191 |
| commutator, socle, cosocle | C23×C191 | C24 |
| Fitting, prime radical | C2×#121×C191 | C2 |
| hypercenter | C2×#121 | D191 |
| hypocenter | C191 | #2436 |
| LCS | G ▷ C23×C191 ▷ C191 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic382 | C2 | semidirect |
| 2. C2×#20259309 | C2 | semidirect |
| 3. #27132575 | C2 | semidirect |
| 4. #27132568 | C2 | semidirect |
| 5. #27132543 | C2 | semidirect |
| 6. C4×C22⋊Dic191 | C2 | semidirect |
| 30. C2×Dic382 | D4 | semidirect |
| 85. C22×C191 | #124 | semidirect |
| 101. C191 | #2436 | semidirect |
| 187. C22 | #20259309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic382 | 2 |
| C2×#20259309 | 2 |
| #27132575 | 2 |
| #27132568 | 2 |
| #27132543 | 2 |
| C4×C22⋊Dic191 | 2 |
| C2×#121×C191 | 2 |
| #2436 | 191 |