Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
2158 conjugacy classes of subgroups; only the 558 normal subgroups are shown.
This group has 2158 conjugacy classes of subgroups — too many to draw. Only its 558 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C107 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C107 |
| prime radical | C23×D4×C107 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#399×C107 | C2 | semidirect |
| 3. C2×#384×C107 | C2 | semidirect |
| 4. C4×#95×C107 | C2 | semidirect |
| 29. #95×C107 | D4 | semidirect |
| 90. C4×C107 | #399 | semidirect |
| 91. #15155 | C107 | direct (N × H) |
| 98. C2×#399 | C2×C107 | semidirect |
| 100. C2×#384 | C2×C107 | semidirect |
| 101. C4×#95 | C2×C107 | semidirect |
| 102. C107 | #15155 | direct (N × H) |
| 127. #95 | D4×C107 | semidirect |
| 188. C4 | #399×C107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#399×C107 | 2 |
| C2×#390×C107 | 2 |
| C2×#384×C107 | 2 |
| C4×#95×C107 | 2 |
| #15155 | 107 |