Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1310 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 1310 conjugacy classes of subgroups — too many to draw. Only its 286 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×C89 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C89 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C89 ◁ C43×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#442×C89 | C2 | semidirect |
| 2. C4×#127×C89 | C2 | semidirect |
| 3. C89×#2094 | C2 | semidirect |
| 4. C89×#2011 | C2 | semidirect |
| 5. C89×#1745 | C2 | semidirect |
| 37. #97×C89 | D4 | semidirect |
| 94. #23802 | C89 | direct (N × H) |
| 99. C2×#442 | C2×C89 | semidirect |
| 100. C4×#127 | C2×C89 | semidirect |
| 101. #2094 | C2×C89 | semidirect |
| 102. #2011 | C2×C89 | semidirect |
| 103. #1745 | C2×C89 | semidirect |
| 104. C89 | #23802 | direct (N × H) |
| 136. #97 | D4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#442×C89 | 2 |
| C4×#127×C89 | 2 |
| C89×#2094 | 2 |
| C89×#2011 | 2 |
| C89×#1745 | 2 |
| #23802 | 89 |