Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
840 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 840 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 | #399×C191 | C2 |
| hypercenter | #399 | D191 |
| hypocenter | C191 | #2397 |
| LCS | G ▷ C23×C191 ▷ C191 | |
| UCS | C1 ◁ C23 ◁ #399 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20259284 | C2 | semidirect |
| 2. C2×(C22⋊D191)⋊C4 | C2 | semidirect |
| 3. #27132598 | C2 | semidirect |
| 4. #27132573 | C2 | semidirect |
| 5. #27132572 | C2 | semidirect |
| 6. #27132508 | C2 | semidirect |
| 7. #399×C191 | C2 | semidirect |
| 37. C4×Dic191 | D4 | semidirect |
| 86. C191 | #2397 | semidirect |
| 91. #399 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259284 | 2 |
| C2×(C22⋊D191)⋊C4 | 2 |
| #27132598 | 2 |
| #27132573 | 2 |
| #27132572 | 2 |
| #27132508 | 2 |
| #399×C191 | 2 |
| #2397 | 191 |