Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
240 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C109 | #466 |
| commutator, Frattini, cosocle | C4×C8 | C23×C109 |
| prime radical | C109×#1667 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C42×C109 ◁ C8×D4×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C109×#2240 | C2 | semidirect |
| 2. D4×C16×C109 | C2 | semidirect |
| 3. C109×#1673 | C2 | semidirect |
| 5. C109×#1371 | C2 | semidirect |
| 6. C109×#1364 | C2 | semidirect |
| 7. C109×#1361 | C2 | semidirect |
| 108. #12467 | C109 | direct (N × H) |
| 114. #2240 | C2×C109 | semidirect |
| 115. D4×C16 | C2×C109 | semidirect |
| 116. #1673 | C2×C109 | semidirect |
| 118. #1371 | C2×C109 | semidirect |
| 119. #1364 | C2×C109 | semidirect |
| 120. #1361 | C2×C109 | semidirect |
| 121. C109 | #12467 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#2240 | 2 |
| D4×C16×C109 | 2 |
| C109×#1673 | 2 |
| C109×#1667 | 2 |
| C109×#1371 | 2 |
| C109×#1364 | 2 |
| C109×#1361 | 2 |
| #12467 | 109 |