Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
840 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D191 |
| commutator, socle, cosocle | C23×C191 | C24 |
| Frattini | C23 | C23×D191 |
| Fitting | C2×C4×D4×C191 | C2 |
| hypercenter | C2×C4×D4 | D191 |
| hypocenter | C191 | #2397 |
| LCS | G ▷ C23×C191 ▷ C191 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×D764 | C2 | semidirect |
| 2. C2×C4×C22⋊D191 | C2 | semidirect |
| 3. #27132599 | C2 | semidirect |
| 4. #27132598 | C2 | semidirect |
| 5. #27132572 | C2 | semidirect |
| 6. #27132571 | C2 | semidirect |
| 7. #27132509 | C2 | semidirect |
| 8. C2×C4×D4×C191 | C2 | semidirect |
| 43. C4×Dic191 | D4 | semidirect |
| 55. C42×C191 | D4 | semidirect |
| 111. C191 | #2397 | semidirect |
| 115. C2×C4×D4 | D191 | semidirect |
| 167. C42 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D764 | 2 |
| C2×C4×C22⋊D191 | 2 |
| #27132599 | 2 |
| #27132598 | 2 |
| #27132572 | 2 |
| #27132571 | 2 |
| #27132509 | 2 |
| C2×C4×D4×C191 | 2 |
| #2397 | 191 |