Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
1074 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 238 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C109 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C109 |
| prime radical | C109×#2867 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C109 ◁ C43×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C109×#2863 | C2 | semidirect |
| 3. C109×#2041 | C2 | semidirect |
| 4. C109×#2014 | C2 | semidirect |
| 5. C109×#1839 | C2 | semidirect |
| 56. C42×C109 | SD16 | semidirect |
| 88. #32798 | C109 | direct (N × H) |
| 94. #2863 | C2×C109 | semidirect |
| 95. #2041 | C2×C109 | semidirect |
| 96. #2014 | C2×C109 | semidirect |
| 97. #1839 | C2×C109 | semidirect |
| 98. C109 | #32798 | direct (N × H) |
| 149. C42 | SD16×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C109×#2867 | 2 |
| C109×#2863 | 2 |
| C109×#2041 | 2 |
| C109×#2014 | 2 |
| C109×#1839 | 2 |
| #32798 | 109 |