Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
952 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 169 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 | C2×#121×C191 | C2 |
| hypercenter | C2×#121 | D191 |
| hypocenter | C191 | #2431 |
| 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. C22×#15690287 | C2 | semidirect |
| 2. C2×#20259318 | C2 | semidirect |
| 3. C2×#20259309 | C2 | semidirect |
| 4. #27132571 | C2 | semidirect |
| 5. #27132568 | C2 | semidirect |
| 6. #27132564 | C2 | semidirect |
| 7. #27132539 | C2 | semidirect |
| 8. C4×C22⋊Dic191 | C2 | semidirect |
| 9. C2×#121×C191 | C2 | semidirect |
| 37. C2×Dic382 | D4 | semidirect |
| 40. C2×D764 | D4 | semidirect |
| 67. C22×C4×C191 | D4 | semidirect |
| 90. C2×Dic191 | #41 | semidirect |
| 148. C191 | #2431 | semidirect |
| 153. C2×#121 | D191 | semidirect |
| 211. C22×C4 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690287 | 2 |
| C2×#20259318 | 2 |
| C2×#20259309 | 2 |
| #27132571 | 2 |
| #27132568 | 2 |
| #27132564 | 2 |
| #27132539 | 2 |
| C4×C22⋊Dic191 | 2 |
| C2×#121×C191 | 2 |
| #2431 | 191 |