Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
944 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 163 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 | #394×C191 | C2 |
| hypercenter | #394 | D191 |
| hypocenter | C191 | #2388 |
| LCS | G ▷ C23×C191 ▷ C191 | |
| UCS | C1 ◁ C23 ◁ #394 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#15690286 | C2 | semidirect |
| 2. C2×#20259284 | C2 | semidirect |
| 3. C2×(C22⋊D191)⋊C4 | C2 | semidirect |
| 4. #27132583 | C2 | semidirect |
| 5. #27132578 | C2 | semidirect |
| 6. #27132576 | C2 | semidirect |
| 7. #27132572 | C2 | semidirect |
| 8. #27132571 | C2 | semidirect |
| 9. C22⋊C4×Dic191 | C2 | semidirect |
| 10. #27132510 | C2 | semidirect |
| 11. #394×C191 | C2 | semidirect |
| 55. C22×Dic191 | D4 | semidirect |
| 63. C2×C4×D191 | D4 | semidirect |
| 91. C22×D191 | #41 | semidirect |
| 106. C2×Dic191 | #41 | semidirect |
| 127. C2×C4×C191 | #41 | semidirect |
| 166. C191 | #2388 | semidirect |
| 173. #394 | D191 | semidirect |
| 294. C2×C4 | #15690286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690286 | 2 |
| C2×#20259284 | 2 |
| C2×(C22⋊D191)⋊C4 | 2 |
| #27132583 | 2 |
| #27132578 | 2 |
| #27132576 | 2 |
| #27132572 | 2 |
| #27132571 | 2 |
| C22⋊C4×Dic191 | 2 |
| #27132510 | 2 |
| #394×C191 | 2 |
| #2388 | 191 |