Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
2826 conjugacy classes of subgroups; only the 478 normal subgroups are shown.
This group has 2826 conjugacy classes of subgroups — too many to draw. Only its 478 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×C109 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C109 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#399×C109 | C2 | semidirect |
| 2. C2×#392×C109 | C2 | semidirect |
| 3. C2×#390×C109 | C2 | semidirect |
| 4. C4×#95×C109 | C2 | semidirect |
| 29. C2×C42×C109 | D4 | semidirect |
| 30. #95×C109 | D4 | semidirect |
| 102. #15172 | C109 | direct (N × H) |
| 109. C2×#399 | C2×C109 | semidirect |
| 110. C2×#392 | C2×C109 | semidirect |
| 111. C2×#390 | C2×C109 | semidirect |
| 112. C4×#95 | C2×C109 | semidirect |
| 113. C109 | #15172 | direct (N × H) |
| 138. C2×C42 | D4×C109 | semidirect |
| 139. #95 | D4×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#399×C109 | 2 |
| C2×#392×C109 | 2 |
| C2×#390×C109 | 2 |
| C4×#95×C109 | 2 |
| #15172 | 109 |