Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
226 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C23 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C2×M16×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#575 | C2 | semidirect |
| 2. C23×#509 | C2 | semidirect |
| 3. C23×#469 | C2 | semidirect |
| 4. C23×#360 | C2 | semidirect |
| 5. C23×#349 | C2 | semidirect |
| 11. C2×D8×C23 | C22 | semidirect |
| 16. C23×M32 | C22 | semidirect |
| 17. C23×#106 | C22 | semidirect |
| 31. Q16×C23 | D4 | semidirect |
| 36. D8×C23 | D4 | semidirect |
| 65. #2190 | C23 | direct (N × H) |
| 79. #575 | C2×C23 | semidirect |
| 80. #509 | C2×C23 | semidirect |
| 81. #469 | C2×C23 | semidirect |
| 82. #360 | C2×C23 | semidirect |
| 83. #349 | C2×C23 | semidirect |
| 94. C2×D8 | C22×C23 | semidirect |
| 99. M32 | C22×C23 | semidirect |
| 100. #106 | C22×C23 | semidirect |
| 102. C23 | #2190 | direct (N × H) |
| 115. Q16 | D4×C23 | semidirect |
| 120. D8 | D4×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#575 | 2 |
| C23×#509 | 2 |
| C23×#469 | 2 |
| C23×#360 | 2 |
| C23×#349 | 2 |
| #2190 | 23 |