Finite Group DatabasebetaFinite Group DatabasebetaOrder 27904.
232 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 78 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 | C2×D16 |
| commutator, Frattini, cosocle | C2×C16 | C23×C109 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C42×C109 ◁ C4×C8×C109 ◁ C4×C16×C109 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D32×C109 | C2 | semidirect |
| 2. C109×#2246 | C2 | semidirect |
| 3. C4×D16×C109 | C2 | semidirect |
| 4. C109×C4⋊C32 | C2 | semidirect |
| 5. C109×#1415 | C2 | semidirect |
| 25. D16×C109 | D4 | semidirect |
| 75. C4×C109 | D32 | semidirect |
| 78. #13685 | C109 | direct (N × H) |
| 84. C2×D32 | C2×C109 | semidirect |
| 85. #2246 | C2×C109 | semidirect |
| 86. C4×D16 | C2×C109 | semidirect |
| 87. C4⋊C32 | C2×C109 | semidirect |
| 88. #1415 | C2×C109 | semidirect |
| 89. C109 | #13685 | direct (N × H) |
| 109. D16 | D4×C109 | semidirect |
| 159. C4 | D32×C109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D32×C109 | 2 |
| C109×#2246 | 2 |
| C4×D16×C109 | 2 |
| C109×C4⋊C32 | 2 |
| C109×#1415 | 2 |
| #13685 | 109 |