Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
214 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 214 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 | #493×C109 | C22 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C42×C109 ◁ C8×Q8×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×C16×C109 | C2 | semidirect |
| 3. C109×#1676 | C2 | semidirect |
| 5. C109×#1372 | C2 | semidirect |
| 6. C109×#1365 | C2 | semidirect |
| 99. #12476 | C109 | direct (N × H) |
| 105. Q8×C16 | C2×C109 | semidirect |
| 106. #1676 | C2×C109 | semidirect |
| 108. #1372 | C2×C109 | semidirect |
| 109. #1365 | C2×C109 | semidirect |
| 111. C109 | #12476 | 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 |
| Q8×C16×C109 | 2 |
| C109×#1676 | 2 |
| C109×#1668 | 2 |
| C109×#1372 | 2 |
| C109×#1365 | 2 |
| C109×#1361 | 2 |
| #12476 | 109 |